In Harry Potter and the Philosopher's Stone, Hermione is in the toilets when Harry and Ron lock in the troll. She lies and says that she went looking for the troll. Why? She could have just said that she was in there because she needed the toilet (she was allowed to be, it's a girls' bathroom) and Harry and Ron came to save her.
Is there a reason she lied?
There's a few things going on here
Hermione wanted to protect her saviours
Recognising that the boys are about to get punished for their actions (disobeying a teacher) while she's going to get away scot free, Hermione's lie gets her into trouble but largely gets them both out.
‘If they hadn’t found me, I’d be dead now. Harry stuck his wand up its nose and Ron knocked it out with its own club. They didn’t have time to come and fetch anyone. It was about to finish me off when they arrived.’
Harry and Ron tried to look as though this story wasn’t new to them.
‘Well – in that case …’ said Professor McGonagall, staring at the three of them. ‘Miss Granger, you foolish girl, how could you think of tackling a mountain troll on your own?’
Her actions demonstrate her forgiveness of Ron
It would have been the easiest thing in the world to have thrown them under the bus "I was in the loo crying because Ron said horrible things to me" but after they saved her life, she felt that she wanted to throw her lot in with theirs and damn the consequences. It worked and they all became friends.
But from that moment on, Hermione Granger became their friend. There are some things you can’t share without ending up liking each other, and knocking out a twelve-foot mountain troll is one of them.
Her actions were logical
As a result of her lie, Gryffindor lost five points but gained ten. Had she said nothing, it's probably that they would have lost at least ten points and possibly many more. Because of her previous good reputation, any punishment she gets is likely to be far less severe.
Hermione panicked and couldn't think of a better lie.
Saying that she went looking for the troll probably wasn't the best thing she could have said. It worked well enough, since she was able to get both Harry and Ron out of trouble and come out of it with five extra House points. If she was thinking more clearly, she might have been able to say something that would keep all three of them out of trouble, and not get any House points deducted.
Remember, though, she probably wasn't able to think particularly clearly. She was having a very stressful day. She was crying in a bathroom all day because Ron insulted her, then she was cornered by a troll. She narrowly escaped being either hurt or killed and ended up getting saved by the same student who was the reason why she was there in the first place and his best friend. At this point, she wouldn't have been thinking as logically as she normally does, because she was probably in somewhat of a state of shock.
But after Ron and Harry saved her, she didn't want to immediately get the two of them in trouble, so she said the first thing she could think of to make sure McGonagall wouldn't punish them. What she said was effective in doing that, and she didn't get in that much trouble for saying she went looking for the troll.
As for whether the lie she told was the best way to handle the situation, probably not.
There's no reason why an excuse involving her just being in the bathroom at the wrong time wouldn't have worked. Keep in mind, we don't know where all the bathrooms are in Hogwarts. They probably aren't very close together, since Dumbledore mentioned really needing one when he found a room of chamber pots (actually the Room of Requirement). Hogwarts is a big place, so sometimes it would take a while to get where you're going. The students were all supposed to be in their common rooms, but if it would have been a while before she got there, this definitely could happen. It would have probably been better for her to say she really needed to go, so she ran off to the nearest bathroom.
Presumably, there would be available bathrooms somewhere near where they would be keeping the students (though it's never said, I'd expect each House common room would have one), since they might have been there for a long time, but depending on how far away the end point was, someone easily might not be able to make it all the way if they had to go before the evacuation. This is a plausible situation that McGonagall could believe, since sometimes you just can't wait to get to a bathroom.
She also could have said she was in the bathroom during the student evacuation, in this case also blaming some kind of illness like stomach flu/diarrhea/anything else that would make someone spend a lot of time in the bathroom, and didn't realize that there was a troll in Hogwarts and that students were supposed to be in their common room. This is fairly close to the truth, avoids mentioning her crying or Ron insulting her, and keeps all three of them out of trouble.
Remember why she actually went to the restrooms: she ran away to hide because she was embarrassed and hurt.
The students had been evacuated and were supposed to be with their houses. Nobody would have believed that she just popped off on her own to toilet. She wasn't where she was supposed to be. She lied because of why:
a) she was embarrassed by other kids
b) ran away because she was embarrassed
c) ended up endangering herself and others because of her running away
To admit to all of that would be a perfect storm of embarrassment, the exact thing she was trying to avoid and hide from in the first place
Hermione was in the toilets (and had been all day) because of her previous encounter with Ron, who said many hurtful things.
Her actions were an attempt to prevent Ron from being scolded by the professors and a way of demonstrating to him that he was forgiven.
