Actually I think I have a pretty good guess what would have happened at last year's TDF if Lance hadn't ridden for Alberto. Because I watched last year's TDF. So I'd say in that "hypothetical" situation he would ride a pretty good showing for himself, a strong TTT, and a savvy break into 3rd place.
I'm not a fanboy, I think his wins weren't clean, etc, but damn I would love to see him win it. Just for the spectacle. In sports I love to feel like I'm watching history. Also because while I respect many of them I'm just not in love with any of the other GC contenders. Evans 2.0 maybe an exception.
But it would really take a lot of luck for #8. On his best day he could not lose time in the mountains. Actually making time on the contenders would require big mishaps, like crashes, allergies, or bonking, not just judgment or tactical errors. The high-end burst just isn't there. Also he's just not the TT beast that he was, it's almost a liability now compared to his main competition. No TTT this year means he misses another couple minutes of time he could put on certain rivals.
I say he finishes 4-6, with the podium being Alberto, Schlek the Younger, and a rider to be named later.