Just a quick answer.

Would dedicated service help with the lag?

Maybe.

Potentially.

The thing you need to remember is that if you're connecting to a dedicated server, then you are a client.

Everyone is a client.

So things can only be as good as client can be, and there will always be that latency and some lag.

However, if the dedicated server is doing nothing but server things and not rendering a whole game world, then it can perform better so that hopefully your experience on client will be better even with bigger factories.

Let's play games.