Can a bastard under any circumstance (other than armed rebellion) become a Lord or for that matter, a King, in Game of Thrones?
I am in the middle of Season 1 & Book 1, please avoid spoilers.
I am looking for a generic answer, so please make any specific character references (i.e. Eddard Stark & Jon Snow) only hypothetically.
A bastard can be legitimized by a decree by the king. The instances of bastard(s) being legitimized that occur or are discussed in later books do not directly address the hypothetical case you've asked about. They do, however, strongly imply that once the king decrees that "so and so is legitimate," they have exactly the same rights (including succession) as if they'd always been true-born.
Yes, if he for example takes the throne by force. Im sure there are other ways too but brute force is one way for sure.
Let's take some examples from real-world history:
Power. A bastard can become a King or whatever else if he accumulates enough power. If you have an army, nobody will call you a bastard any more.
Adoption. In history, a lot of kings/lords without direct male heirs adopted a boy and made him a heir. It could be a nephew, a distant cousin but also a bastard. A typical method was to officially proclaim the bastard as a "distant nephew" and then adopt him as son.
Tradition. Every noble house (including the different ones in GoT) is bound my traditional rules which tells you who inherits the title (and everything else). For example, the husband of a female heir can inherit the title if there are no male heirs. In some noble houses, bastards have the same inheritance rights as legal sons (for example, medieval Wales is a prime example). In GoT we don't have enough information about all the noble houses to eliminate this possibility (definitely not valid for the house of Starks).
Marriage. See 3. A bastard can easily become a Lord through marriage.
Tribute/Service to the King. Every noble house starts somewhere. For example, to become a Lord, you would only have to pay enough money to the current King (Kings always need more money) or to serve him well (e.g. save his life in a battle).
The following is not a spoiler for any of the main ASOIAF books or the GOT TV show, but some interesting backstory (about things that happened long before the main story) GRRM has revealed in an interview. I have also included a link to A Wiki of Ice and Fire; the linked page itself doesn't contain any other spoilers, but I wouldn't click on any other links on the wiki.
When Aegon conquered Westeros, his bastard half-brother Orys Baratheon defeated the Storm King Argilac, took his land as Lord of the Stormlands and his daughter for his wife, and became the founder of the Baratheon dynasty.
Bastards cannot legally inherit the titles of their parents/grandparents.
They may inherit only if they are:
AND
Example here would be Addam of Hull and his brother Alyn of Hull who were legitimised by Rhaenyra Targaryen and Alyn later inherited Driftmark from his grandfather Lord Corlys Velaryon (Corlys was in fact their father but he told everyone that the boys were bastards of his late son Laenor perhaps to avoid angering the Royal House since his wife was Princess Rhaenys Targaryen). Another example is Ramsay Snow.
However this is only about inheritance, if a bastard is either granted the title by his liege Lord or he usurps a title by force of arms, they may hold their lands in their own name.
An example would be Benedict Rivers. He was a bastard of Houses Bracken and Blackwood. He became a great Knight and eventually defeated all the Petty Kings of Riverlands and Crowned Himself the King of Trident and founded his own dynasty, House Justman. The House ruled Riverlands for Three centuries until they were deposed by the Storm Kings.
Another Example would be Lord Orys Baratheon. He was a bastard half-brother to Aegon I Targaryen who granted Orys the Paramount Lordship of Stormlands. Since he was never officially acknowledged by Lord Aerion Targaryen nor legitimised by his royal brother, Orys founded his own dynasty, the Baratheons who eventually deposed Aegon's descendants in the aftermath of Robert's rebellion.
Yet another example would Daemon Blackfyre. He was born a bastard to Princess Daena Targaryen and King Aegon IV, named Daemon Waters. When his father gave him the ancestral Targaryen sword Blackfyre and lands of his own, Daemon discarded his bastard surname and chose the name Blackfyre for his own dynasty. Later even when his father legitimised him, Daemon never forsake his own name and never called himself a Targaryen.
It would be good to point out another example of a bastard becoming kind of a Lord
Spoilers for the end of Storm of Swords:
Jon Snow, who is a bastard, is chosen as Lord Commander in The Wall.
It isn't exactly the same a Lord, but it is a really high position, even for someone who isn't a bastard.
...and we have at least two examples.
Ramsay is the bastard son of Roose Bolton. In season 4 Roose had a decree from the crown made up to legitimise Ramsay.
Roose: The North is larger than the other six kingdoms combined. And I am the Warden of the North. The North is mine. Now tell me, what is your name?
Ramsay: Ramsay Snow.
Roose: No, not Ramsay Snow. Open it. From this day until your last day, you are Ramsay Bolton, son of Roose Bolton, Warden of the North.
Game of Thrones, Season 4 Episode 8, "The Mountain and the Viper"
Upon hearing Walda Bolton, Roose's wife, has given birth to a baby boy Ramsay stabs his father and kills him. At this moment Ramsay becomes Lord Bolton.
Ramsay: Maester Wolkan, send ravens to all the Northern houses. Roose Bolton is dead. Poisoned by our enemies. How did he die?
Maester Wolkan: Poisoned by his enemies.
Lord Karstark: You're talking to your lord. Use respect.
Maester Wolkan: Forgive me, my lord.
Game of Thrones, Season 6 Episode 2, "Home"
Jon is the bastard son of Ned Stark.
He's not but he is widely believed to be.
After leaving the Nights Watch on grounds of having died he takes over Winterfell and the North in the Battle of the Bastards against Ramsay Bolton. After the battle he becomes the King in the North.
Lyanna: Your son was butchered at the Red Wedding, Lord Manderly. But you refused the call. You swore allegiance to House Stark, Lord Glover, but in their hour of greatest need, you refused the call. And you, Lord Cerwyn, your father was skinned alive by Ramsay Bolton. Still you refuse the call. But House Mormont remembers. The North remembers. We know no king but the King in the North whose name is Stark. I don’t care if he’s a bastard. Ned Stark’s blood runs through his veins. He’s my king from this day until his last day.
Manderly: Lady Mormont speaks harshly and truly. My son died for Robb Stark, the Young Wolf. I didn’t think we’d find another king in my lifetime. I didn’t commit my men to your cause ‘cause I didn’t want more Manderlys dying for nothing. But I was wrong. Jon Snow avenged the Red Wedding. He is the White Wolf. The King in the North.
Glover: I did not fight beside you on the field and I will regret that until my dying day. A man can only admit when he was wrong and ask forgiveness.
Jon: There’s nothing to forgive, my lord.
Glover: There will be more fights to come. House Glover will stand behind House Stark as we have for a thousands years. And I will stand behind Jon Snow… the King in the North! The King in the North!
Game of Thrones, Season 6 Episode 10, "The Winds of Winter"
The king would have the power to grant any title to anyone he chooses. It may be strange to grant the title of Lord to a bastard, but not impossible.
In book one (stop reading if you are not most of the way through) the king offers a lordship to anyone who could kill the Targaryens. This would mean that if a bastard killed them that bastard would become a lord.
Considering that
"King" Joffrey "Baratheon", who is not only a bastard but a product of incest, sits on the Iron Throne
as of the end of the first book: yes, it is possible for a bastard to rise to high rank.
More generally this can be formulated as: don't let people know that he's a bastard.
Father of the said bastard could always legitimise the bastard by acknowledging his progeny by giving his name to his son/daughter.
Also if the bannermen do not like the way of succesion they could always agree to legitimise the bastard.
