randyhat
I wouldn’t use a sub larger than 2 x 8" max or at a pinch a very fast servo controlled 10" sub. As your crossing over from a 5.25" driver.
12" or 15" subs will be too slow to mate properly. I would also try blocking the port on the LS50 and going for around 100hz xover.
https://www.stereophile.com/images/1212KEF50fig3.jpg
And best maybe use two "tall" (24") subs and use them as stands for the LS50’s, like these I use, magic old Yamaha’s with servo control with linear amps
http://www.audioreview.com/product/speakers/subwoofers/yamaha/yst-sw305.html
Cheers George