Lindsay Lohan -- Bar Fight Over Max from 'The Wanted'

Lindsay Lohan punched another woman in the face over Max from the boy band "The Wanted" last night ... and we've learned Max was turned off by the fact LiLo was sloppy drunk inside the club ... this according to sources at the club.

We're told ... Lindsay went to the Justin Bieber concert -- but not to see the Biebs -- "The Wanted" was the opening act ... and Lindsay has been scoping Max out for the last few days.

She's not the only one either -- on his way out of his NYC hotel yesterday, Max was swarmed by adoring female fans ... and he even kissed a few.

Sources say Lindsay tried to get backstage after the concert to see him -- but she was blocked. Fast forward to later that evening when Lindsay met up with Max, Jay and Tom at a hotel bar.

The four of them -- along with one of LiLo's friends -- then went to the club Avenue together.

As the evening wore on, we're told Lindsay got drunker and drunker ... and it turned Max off. He then started talking to another woman, which enraged Lindsay. That woman is the one Lindsay is accused of battering. (FYI -- Max was also really drunk).

Ironically, Max washed his hands of both of them -- found another girl in the club -- and went home with her instead ... while Lindsay ended up in jail.