Usually, when a girl, lies on a guys bed, it's like an invitation to have sex, or at least, that's how most guys will see it.
So I'd say, most guys, would have no problem, with their girl, lounging on their bed.
But if you have just met then, best if you are in his place, is to sit on a chair.
If there is no other suitable seating arrangement, then just sit on the bed, and don't lounge on it.
Unless of course, you do want to send him a message. That you want to do more than just lounge on the bed.
I think it send mixed signals that you are ready to get busy.
when I met my BF I didn't go to his place or invite him to mine until after almost 3 months and after he'd said he loved me, wanted me to meet his mother, asked me to be his girlfriend and after a lot of dates.