As noted, yes, but Lana will break up with you, and, like Koth and Theron, but unlike any other jilted companion(1), she will give you a mission called (for Lana) Things Left Unsaid, where you and she will have that talk that ends it for good (no, it's not recoverable). From what people have said, and from the no-sound videos I've seen on YT, it's not a happy time for anyone.

(1) The other breakups occur as:

* An actual conversation in a mission where a companion returns and you say that it's over. I've only done Aric Jorgan's version of this(2), and he was essentially in denial (duh, his wife just told him she's not interested any more - he has yet to find out at that point that she had shacked up with a lady Sith).

* An email where you break off a companion's romance by starting one with someone else.

(2) Well, there was that one agent who pursued both Raina Temple and Kaliyo, and had "that" talk and broke up with Raina. She was not a happy camper.