Yeah, that should be enough. When you say split screen, do you mean extended onto the second monitor, or duplicated? Also are you sure that it only lags when connected to the monitor. This is odd.
check your battery settings, i was laggy and i didn't know why, then i remembered my setting was on power saver, if that be the case, then change setting to either balanced or high performance.
Without the monitor connected, close all open programs and go into ask manager and then the processes tab. Do you see anything taking up a large amount of RAM or CPU?