In this reddit post below it seems that a player did indeed find a phantom in NG+ and kill it receiving a skirt from the enemy.
Quote from the poster Poo_Tsunami:
"I found a painting guardian in Aldia's keep! Probably old news but I haven't seen this mentioned anywhere so I thought I'd take a picture of the item it dropped and the description. I didn't have time to snap a picture of the actual phantom because it was trying to kill me.
From the back
From the front
Although the description makes no mention of guarding paintings, the armor is exactly the same and the phantom was hiding behind a painting dual wielding square blades."
So yes it may be possible to obtain the lance he was using.
There is a list in the link below that tells you how to acquire each regualar lance in the game. If it was another normal players lance he was using you should be able to identify it.
(I'd also like to note that this is NOT one of the npc invaders.)
List of NPC's