I don’t understand what you mean by moving off. How are you trying to attach the Li foil? Are attempting to diffusion bond it by heating or what is the process? I understand the Argon atmosphere because Li is very reactive with O2 (air).
What is the Cu thickness and how thick does the Li coating need to be?
I would try melting the Li in a ceramic crucible obviously not because of temperature but to preclude alloying the Li with a metal or alloy crucible. And then dip the Cu as you suggest
If the Cu foil can be thick enough, you could machine or stamp a pocket into the Cu then use the Cu as a crucible to melt the Li directly with hopes of bonding. But I think you will very likely require a flux as you suggest. You might get some help with flux from Handy and Harmon Company. Also you might need to use a dry Hydrogen atmosphere instead of Argon in which case you will need a sealed retort but (for SAFETY purge with Argon or Nitrogen gas before) purging with Hydrogen.
Is it possible to electroplate the Li onto the Cu?
Design for RELIABILITY, manufacturability, and maintainability