Tomb raider was a great movie, I honestly dont see how you people didnt like it? Though i know that people are entitled to their own opinion... I feel the movie lacked romance, the movie would have been better with a little romance, but thats just my opinion. I mean, did alex and lara get together? you dont know, and that was kinda misleading.
I also am a fan of the movie, I have played the games a for a short time and I thought the movie got across the actually character that she is. To answer your question about alex, though it isnt entirely clear in the movie somewhere in the special features or something I read I remember it saying how Alex was sapost to be like a boyfriend of hers or something. Not exacutally sure but it could of been a relation ship that was strong in the past and wasnt as strong in the point of the movie, or maybe they were split up at the time or something. If you want Romance I would recomend the second tomb raider (Tomb Raider: Cradle Of Life) Though it dosnt have a great deal of romance it has more than the first one. And acording to the second movie, aparently alex and lara never got together, or did for a short time or something, I guess they leave it for your own amagination to make it what you want it to be.