TS,
I have been in a somewhat similar position.
You've scored an own goal by saying she's lonely... yes, as someone
has said, asking her if another guy is dating her will provoke a
"hey, it's none of your business, we are not an item"
response.
But I would like to point out that even if you didn't score that
own goal, you're already losing at 2-0 down with 5 minutes to
fulltime. So, I hope that's a consolation thought.
Guys usually get very attracted to pretty girls, and like someone
else said, you're just mourning a loss of a very attractive close
friend. After all, defeat is always bitter. It sucks to walk off
the field with a 3-0 result against you after all that effort. But
hey, there's always another game, or girl, to look forward
to.
Outrageously pretty girls like her feel entitled to use guys for
emotional support, and after they have recovered, if they feel that
the guy is not a good relationship investment, given the view that
they are entitled to the best guys (character, money, brains, body
...) with their looks, they will dish out the "get lost"
look.
Think of it as a good deed you have done to her, and the coolest
response from you is to feel nothing against her in weeks and
months to come.
May you find the right girl who desires your love.