Lindsey Vonn -- 2nd Date with 'Vikings' Star ... Finally More than Friends?

Seems Alexander Ludwig is ferociously battling his way out of the friend zone -- 'cause the "Vikings" star was out with Lindsey Vonn AGAIN ... despite the fact she claimed they were "just friends."

Vonn and Ludwig got some people talkin' earlier this month when they hit up a fancy West Hollywood restaurant together. But days later, Vonn insisted there was nothing romantic about the date.

Fast forward to Wednesday night ... when the 'Hunger Games' star showed up to the Clippers game at Staples Center -- WITH VONN!!

So ... did 23-year-old Ludwig finally convince the 31-year-old stunner to give him a shot???

Vonn did sorta leave the door open when she was talking about Ludwig a few weeks ago.

Good luck ...