Just in case anyone else experiences a similar issue, I just wanted to update this post before it is closed.
I raised a ticket with Support, who have been brilliant in helping me with this issue. They assisted me in using some tools to send them some data, recorded while I was experiencing the lag and freezing.
The solution was to delete the %LOCALAPPDATA%\CCP\EVE\ folders (be aware, doing this clears the cache and all in-game settings). I performed another fresh install of the game at the same time, to cover everything. Upon logging back in, the lag and issues I were having are completely resolved.