During Act 1, when I went to dismiss Lae'zel from the party, the conversation took a sudden turn when she bluntly asked if I wanted to sleep with her. If I say yes, am I locked into a relationship with Lae'zel? Will this lock me out of romancing other party members?
No, it will not. In general, it is possible to abort the romance plotline with most companion characters through a "break up" dialog option that is almost always available when talking to them. Afterwards you are able to pursue a relationship with any other companion, provided that it is still early enough in the game's story for the relevant relationship event triggers to occur.
There are a couple exceptions, though. For example, the relationship with Astarion becomes permanent if:
the player decided to let him ascend after defeating Cazador and then decides to become Astarion's vampire spawn.
There are also a couple situations that allow to romance multiple characters at the same time (and no, that's a feature and not a bug). However, as far as I could find, Lae'Zel isn't a part of any of those poly-romance routes.
Oh, and no matter who you are romancing, you will be able to cheat on them with
Mizora, your spirit guardian, the drow prostitutes in Sharess' Caress and/or Raphael's minion Harleep.
Will you get away with that?
Nah, not spoiling that :)