I was considering allowing the use of Lance of Lethargy so that each impact from an Eldritch Blast could reduce the speed of creatures multiple times in the caster's turn.

For example, if a warlock creates 3 beams and each beam hits the same creature, it would reduce that creature’s speed by 30 feet until the end of the warlock's next turn.

Could this unbalance the game too much in some way or in some circumstance?

If you are ok with your enemies routinely having 0 movement speed while trapped far away from the party go for it.

Quote from tarodnet >>

I was considering allowing the use of Lance of Lethargy so that each impact from an Eldritch Blast could reduce the speed of creatures multiple times in the caster's turn…. Could this unbalance the game too much in some way or in some circumstance?

 
Short answer, “yes.”

Ok, ok, guys, thank you very much for your answers! I won't change a bit of this invocation, then 😅

You should feel free to change anything you like. We’re just letting you know that you should be prepared for the consequences is all. Besides, with Lance of Lethargy and Grasp of Hadar, that’s 20 feet of movement right there, and there’s no rule that says you can’t use both on the same hit.

Quote from IamSposta >>

You should feel free to change anything you like. We’re just letting you know that you should be prepared for the consequences is all. [...]

I know, I know! That was my goal, really, to know your opinion based on your experience.

I really appreciate your answers ❤️