Just to clear up some terminology:
"Lag" in this context is usually reserved for delays due to network latency. The main things here involve network speed & stability, as well as how much data you have to transmit between server/clients.
"Frame rate drops/low frame rate" is usually reserved for the game playing at a low frame rate. This can be caused by having too much performance heavy AI or calculations (CPU bound), or by trying to draw more than the client's computer can reasonable handle (GPU bound) -- or a mixture of the two. This will vary wildly based on the player's hardware. The only reasonable thing you can do here is set a minimum requirement, and test the game on that hardware. There are things you can do to help some of these issues (GPU especially), by allowing different render resolutions, post-processing effects, etc.
Asset load time would mainly impact frame rate, but there's not always a strict correlation. A game with a 2 minute loading screen can have better performance than a game loading for 1 minute.
Generally, it's hard to say "this will make the game too slow" -- a lot will depend on the actual implementation.
Set a target hardware, and test regularly on it. If the game runs too slow, use profiling techniques to figure out why it's too slow. Maybe there's code you can optimize to make the problem go away, or maybe you just need to make the assets more light-weight. There's no 1 true answer here. It will depend on what you have and what you're doing.
