DPI is only relevant if you intend to print.

I admit that I don't use any specific size for the map, probably because they are not for printing. (I did one that was something like 3000 x 12 000)
But for comparison : A4 at 300 DPI is 3508 x 2480. So 4000 x 4000 is somewhat larger than a standard european sheet.

2 GB is the size of the file when you are in Windows or it's the size indicated size while in Photoshop? The value is Photoshop is always strange.
2 Gb is kinda big in my opinion. I assume you are using a lot of textures? If yes, that is the reason why it lags. The pixels of each layer needs to be stored. If you have several complex layers, that's a lot of pixels.

I'm not sure if the lag is related to the CPU or GPU.