I would try flux. it helps wick solder to materials which otherwise won't 'take' solder (usually because of heat issues).
this V is specifically for aluminum but it's flux and it can help.
Aluminum Solder Flux 2oz Bottle | eBay
the problem with dipping the CCA in a soldered lug.. is the fact that without flux, the solder still won't wick to the strands.. and any bond you make that way is only the mechanical bond of the solder keeping the strands there.
I hope this makes sense.