A lance is a one-handed weapon, so yes, it can be an Armblade
I asked the following question "Are lances and nets and versatile weapons considered one-handed weapons?" and the current answers there both state that lances are in fact one-handed weapons. This is because they do not have the Two-Handed property. The only requirement for the Armblade is that it be "any one-handed melee weapon" which the lance qualifies as. The mechanical effects of an Armblade are as follows:
[...] As a bonus action, you can retract the armblade into your forearm or extend it from there. While it is extended, you can use the weapon as if you were holding it, and you can't use that hand for other purposes.
- Eberron: Rising from the Last War (page 276)
This means that you could use the weapon as if you were holding it, and as this requires a one-handed weapon, that would be as if you were holding it in one hand.
Armblades do not change any properties, requirements, or mechanics of their chosen weapon
Note that the Armblade also does not change any of the chosen weapon's properties, so it could still be wielded in two-hands if the weapon were versatile, or in this case, the lance which would also retain it's Special property:
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.
This means that you could not actually use the lance one-handedly unless you were mounted, effectively making your hand entirely useless unless mounted as it cannot be used for anything else.