How did Voldemort know Lily didn't have her wand?

I think Voldemort was guessing based on what he’d already seen of the house.

I’m assuming that Harry’s dream in this chapter is an accurate account of Voldemort’s thoughts on the night that he killed Harry’s parents. Whether Voldemort’s assessment was accurate might be up for question, but I think he could be reasonably sure that Lily was unarmed.

All the information we need comes from this passage.

It starts as Voldemort approaches the house. He can see into their living room, which is when he sees James cast his wand aside, and Lily pick up Harry:

A door opened and the mother entered, saying words he could not hear, her long dark-red hair falling over her face. Now the father scooped up the son and handed him to the mother. He threw his wand down upon the sofa and stretched, yawning….

Since Lily is holding Harry, it seems plausible to assume that she was unarmed, which Voldemort would have seen. (He may also have seen her wand lying somewhere in this room, but it isn’t mentioned and would be hard to spot without some sort of helpful indicator.)

When he enters the house (through the front door, presumably), James runs out into the hallway:

He was over the threshold as James came sprinting into the hall. It was easy, too easy, he had not even picked up his wand….

So James, the defender of the house, didn’t pick up a wand that was feet away. Presumably if Lily’s wand was somewhere in the room, she left hers as well.

The killing of James gives us important information about the layout of the house:

The green light filled the cramped hallway, it lit the pram pushed against the wall, it made the banisters glare like lightning rods, and James Potter fell like a marionette whose strings were cut….

If the banisters are in the hallway, then so are the stairs. This means Voldemort must have glimpsed Lily as she carried Harry upstairs, and seen that she was wandless.

When he gets upstairs, and hears her stacking things against the door, it confirms that she doesn’t have her wand. He’d hear her moving around the room, whereas a witch would use a spell.