I saw a meme that was joking around about Lithium and Argon bonding (see pic below). It got me wondering: Can Lithium and Argon bond in any circumstance?
It's no joke; a gas-phase lithium-argon diatomic molecule does exist. However, it (and about two dozen other di-atoms having various elements bonded to the argon) is considered to be bound only by a van der Waals interaction. See the list of diatomic van der Waals molecules here.
Argon is a noble gas. This means that it does not simply "bond" with anything. These gases have a very strong resistance to joining with other atoms. So, to answer your question, no, you can not bond argon and lithium under any circumstances. Anyone who says they have done so is a LiAr.
Also, since lithium is highly reactive and flammable and argon is used in neon, I would not suggest trying to combine these two without a proper location and gear.