I think if Connor Williams were to drop, they'd take him at 23. But he might be the only real possibility of LT in round 1.
Miller, from everything I've read, is a round 2, maybe even round 3 prospect.
Rams are more likely to go OLB/Edge rusher, ILB, or NT.
I know some are pushing for Vea, but there is no way that guy lasts until 23. But Payne? The boards I see make it at least 50/50 that he could be there. And because I'm an SEC fan, I see Payne play quite a bit. He is a beast. Quick, but not fast. Country strong. Immovable. I think he'd be a terrific NT for the Rams.
All that said, I can't imagine that the Rams don't have their eyes on a couple of Edge Rushers that they'll be crossing their fingers will fall to them.....or Les may move up a bit to get one.