dnd-5eeberronmagic-itemsweapons
In Eberron: Rising from the Last War, an Armblade is a magic item that can be "any one-handed melee weapon". With there not being an actual one-handed trait, it's assumed that melee weapons that don't require two hands to use can apply. But lances have the "special" property, which states that a lance "requires two hands to wield when you aren't mounted."
Does this mean that a warforged could have a lance armblade? What limitations would be imposed on it when used when not mounted?
If you're willing to go outside the Player's Handbook for clarification, a reach weapon does work a little differently for a rider atop a mount: a reach weapon becomes a little more versatile.
The Player's Handbook only says, "For simplicity, assume that you share your mount's space during [mounted] combat" (157). The handful of times creatures otherwise share spaces the creatures are foes (like during a grapple), the creatures are all really little (like a gang of grigs) or one creature's very big and the others littler (like an ogre and a gang of grigs), or one creature's helpless (like when one's dead). Because those all have clear rules and this case doesn't, precisely what the Player's Handbook actually means when it says a rider and mount share the mount's space is up to the DM. With its silence, the Player's Handbook implies that—much like if the rider's mount were wielding the reach weapon instead—a rider wielding a reach weapon is burdened with the reach weapon's lack of close-combat functionality. And, as you may've noticed, this kind of sucks.
St. George behaving ambiguously under RAW.
Now, let me preface this next part by saying that the Rules of the Game columns by Skip Williams—a coauthor of Dungeons and Dragons, Third Edition—take some heat because the columns sometimes present wrong information. (For instance, this column had to be reposted because of errors.) Yet in this case, instead of creating a new rule (which the columns sometimes do), the column clarifies the above ambiguous one. The Rules of the Game Web column "All about Mounts (Part One)" says
For all game purposes, you and your mount function as a single unit on the battlefield. Your mount continues to use its own space and reach while carrying you. You effectively use your mount's space and your own reach (or whatever extended reach your weapon gives you) while mounted. While you're mounted, any attack that can reach a square in the space you and your mount jointly occupy can affect you or your mount (it doesn't make a difference which square). Likewise, you measure your reach for your melee attacks and the range for your ranged attacks from any square you and your mount jointly occupy. You don't get cover from your mount unless you use the Ride skill to get it, and your mount doesn't block your attacks and provide your foes with cover.
(Emphases mine.) So, while I expect most folks (like me!) imagined a typical reach-weapon-wielding rider threatening the 10 ft. around the typical mount—and leaving that pesky unthreatened usually-5-ft. gap between the reach weapon's threatened squares and the mount so that the mount must defend itself—, this ruling allows a reach-weapon-wielding rider to, essentially, threaten through the mount so that he can also launch attacks against adjacent foes. (While the first emphasized statement's important, the second seals it: a creature can't make attacks of opportunity against foes with relative cover, and if, for example, a rider measures from the farthest-away-from-the-foe square of his mount through the mount, the Player's Handbook's unclear if the mount's granting the foe cover because rider and mount share the mount's space; this ruling clears up that the mount doesn't grant the foe cover from the rider.) St. George approves.
Keep in mind there's still an area into which a typical reach-weapon-wielding rider atop a typical mount can't make attacks: within his and his mount's shared space! The Dungeon Master's Guide says that "a creature can attack into its own space (unless armed with a reach weapon)" (29). (Emphasis mine.) Beware gangs of grig highwaymen! (But only because they're so adorable.)
Let me make clear that I, too, don't like this ruling's provenance, but mounted combat is so vague in the Player's Handbook that relying on an outside source—even a Rules of the Game column—to make heads or tails of it seems better than giving up and playing Smash Bros.
That was long and complicated. These two'll be quick. I swear.
A typical creature wielding a lance one-handed deals the lance's damage plus the creature's Strength modifier. A typical creature wielding a lance two-handed deals the lance's damage plus 1½× the creature's Strength bonus (also see here). This amount doesn't change if the typical creature's riding a typical mount, although usually a creature can't wield a lance one-handed when not riding a mount (see below).
Sure. While a lance is usually a two-handed weapon as per Table 7–5: Weapons (PH 116-7), the Player's Handbook also says, "While mounted, you can wield a lance with one hand" (118). Thus, a mounted rider can use a lance either one-handed or two-handed like St. George up there (although, really, St. George may be using a longspear, which is two-handed, mounted or not). A lance gains—not loses—versatility when a rider's mounted.
Being mounted is very different than flying. The Lance specifically requires you to be mounted in order to avoid the penalty for one-handed use. Mounts are covered in the PHB (page 155), and nowhere does it state that flying/swimming/walking yourself would ever qualify as a mount.
In order to be able to wield a Lance one-handed without disadvantage, you would need a legitimate mount that you are actively riding.
Best Answer
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:
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:
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.