RAW, it seems so
As you have pointed out, the Hex Warrior class feature of a Hexblade Warlock requires the weapon to lack the two-handed property.
From Xanathar's Guide to Everything, pg. 55:
Additionally, whenever you finish a long rest, you can touch one weapon that you are proficient with and that lacks the two-handed property.
The lance does not have the two-handed property, which according to RAW, would make this a valid choice.
However, the lance does have the "Special" property, which says (PHB, pg. 148):
Lance. You have disadvantage when you use a lance to attack a target within 5 feet of you. Also, a lance requires two hands to wield when you aren't mounted.
Although this weapon appears to function as a two-handed weapon, since it lacks that property, we cannot know what the designers were thinking when they made this choice, so as it stands, it is a one-handed weapon that must be used with two hands unless you're mounted.
Although I will say that, although it may count as a valid weapon RAW, it would be reasonable for a DM to rule that you can only use your Hex Warrior class feature (i.e. can attack using CHA) when mounted, otherwise you would have to use STR to make your attack rolls with it when not mounted.