Can a Hexblade warlock choose a lance for his Hex Warrior weapon?

The lance description says:

a lance requires two hands to wield when you aren’t mounted.

Note that the lance lacks the two handed property but still need 2 hands to wield.

The Hexblade warlock’s Hex Warrior feature description (Xanathar’s Guide to Everything, p. 55) says:

Whenever you finish a long rest, you can touch one weapon that you are proficient with and that lacks the two-handed property.

Can I use the Hex Warrior feature with a lance?