Light Fingers is an incredible story. Its central theme is Love, which is coincidentally the central theme of the entire FLverse, so it is quite a fitting storyline. It can turn your character from an unrepentant thief to a truly good person, or from a well-meaning meddler into an absolute monster who works only for the Greater Good, whatever that means to them. I don’t want to spoil too much, but it makes doing what is objectively a truly horrible thing for people in the future into seeming like the only good option. I cried after I finished Light Fingers. But, aside from all that, it can also be cute and heartwarming, and I think that the supporting characters are some of the best in the game. (as well getting the best Ambition lab assistant)
I’ve also played BaL, so I can propagandize for that too. It’s a fun story! It’s perfect for a Seeker! You get to beat up an entire island of nuns to convince them to train you! It has interesting overlap with the Fate-Locked Foreign Office content! And BaL’s highs are very high. But it also has a lot of slow bits, due to a great deal of (I think unjustified in-universe) grinding. But aside from a few parts where it prods at interesting themes, it isn’t nearly as well-rounded or good of a story as Light Fingers. However, I also think it’s the most Fun of all the Ambitions. Do you want a light adventure romp? Then BaL is great! But if you’re looking for something consistently deeper, I’d avoid it.