It sounds to me like you're looking for a stage piano, but I don't know any stage piano with a synth lead patch, though...
My favorite stage piano, and the one I would recommend is the Yamaha CP33. The action is close to perfect, and the piano and string sounds are gorgeous. It does have a Jazz Organ as well, but I don't really like it that much, and it does lack a lead sound. But like I said, I don't know any stage piano with a lead sound.
There are quite a lot of stage pianos out there, though, you can try searching
www.zzounds.com or
www.thomann.de to find the one you're looking for. Atleast it's a starting point