After the Shadow War, Lyta Alexander ran out of money and could not earn a living as a freelancer because she was a rogue Telepath. If she cannot find jobs with humans, she can always find a job with the Aliens. There should not be any problem to earn big bucks given that she is the most powerful Telepath in the universe after being modified by the Vorlons. Besides, she is probably the most attractive female on Babylon 5 and even the religious G'Kar couldn't resist her. G'Kar once made her an offer to mate with her to produce telepathic Narns. How convenient. Londo once offered her lots of money to learn about her experiences with the Vorlons. There should be ample opportunities for her to get rich as long as she opened up her services to the aliens. Why didn't she?
Most of the options you list for her are not terribly appealing.
- The alien market has their own telepaths.
All those telepaths that were recruited and survived the Shadow War, just like Lyta? All trying to work that same market. Minbari and Centauri are confirmed to have their own teeps; they would do business with their own kind, or work through the ambassadors that have their own contacts and resources for verifying the transactions. The rest of the League races may or may not have telepaths, but every alien mind would be a new adjustment Lyta has to make, since most races think differently (established all the way back in Legacies). All that said, Lyta probably is working such non-human jobs where she can, it's just not lucrative enough to sustain her without the Vorlon paying her rent, or the support the command staff enjoy, which Bester points out:
It's just a little one-sided, isn't it? I mean, Sheridan and the others, they have this whole support mechanism. They draw their salary from the docking fees paid by alien ships. Their meals and clothing are all free.
She's actually trying to work on the alien angle with the human corp she's interviewing with at the beginning of the episode:
Lyta: And from 2247 to 2257 I was the commercial telepath for Xenocorp. I monitored their negotiations with representatives from Centauri Prime, Narn and Pak'ma'ra.
So scanning alien minds doesn't bother you?
Well, it's not comfortable. I don't think any of us enjoys it but you get used to it.
Naturally, this falls through as soon as the agent gets the whole picture, because their financial backing is entirely dependent on Psi Corps certification. Alien businesses might not have that limitation, but again, harder market to break into than you might think.
- She rarely can get full power
The blocks and compulsions the Vorlon installed on her vast telepathic power remain in place unless at great need - it's not like she can call them up at will, at least not until later in Season 5, and then she has an entirely different set of problems. She does state she's stronger and can reach farther to Garibaldi, and Bester notes that she's obviously no P-5 anymore, but she's not whipping out doomsday level telepathy on a whim. Besides, the main certification agency for the power of human telepaths would be... Psi Corp. Good luck getting them on board.
- G'kar's offer wasn't attractive before and it's still not now
G'kar was only offering money for basically using Lyta as a lab rat, and he wasn't all that subtle about the alternative more appealing to him, breeding stock and sex toy. Lyta's not going to give up her life just for a paycheck. She does consider this later (again, Season 5) when she has a lot more to gain from the offer than money.
- The Vorlon keep their secrets
Lyta has several memory blocks on her time with the Vorlons, and what isn't explicitly blocked, she's clear about keeping to herself. She is still loyal to the Vorlon, or more specifically, to Kosh. She's not going to sell their secrets. She doesn't tell unless there's urgent need (as @Valorum noted in comment, this happens in Thirdspace, and those were secrets programmed in). She's not going to sell secrets to the highest bidder, and certainly not to Londo, who was as far from the Vorlon as could be.