In reply to:
...trying to move all my live apps from Apache to Lighttpd on the fly would not go so well.
There's absolutely no reason it wouldn't go well.
In reply to:
I'm running WordPress, PhpBB, and Media Wiki on my PS.
None of those are reliant on fcgi perl scripts that would require modification.
In reply to:
If its possible to run both at the same time...
It is. But you can't bind both Apache and Lighty to port 80 simultaneously.
The only thing that would possibly change with your setup is that if Lighty doesn't bind to port 80 then your user's will see something like domain.com:81/index.php in their address bar. If DreamHost have the webserver switch setup so that Apache completely disappears and Lighty binds to port 80 then the change should be positively seemless. You can either ask them if that's the case or just hit the switch and see for yourself.
You can always switch back 
How To Install PHP.INI / ionCube on DreamHost