Change is always good when you feel something is lagging, so just changing up your routine will probably help.
One suggestion to help break a benching plateau is to NOT bench at all for a month or so. I got over one benching plateau in the past by hitting my chest with DB presses (both incline and flat) and weighted dips (these will help grow triceps as well). When I got back on the bench again a month later, I soared through my previous best. That taught me personally not to be so focused on benching, but CHEST development instead. I now only bench once every two or three weeks, and even then many times it's only incline, not flat, as I see better growth this way.
And, yes, strong triceps are critical for big benching. You never see some guy with toothpick arms putting up serious weight, the guys benching big look big everywhere up top - including upper back. Keep in mind the stronger your triceps and back are, the more stable you will be pushing heavier weight, so maybe working on both those areas are what is needed. One suggestion for tricep development - don't use too many cable excersizes - I personally only use one out of three or four excersizes on the cables, the other two or three are with DB (behind the head tricep extensions or one armed extensions bent over a bench) and close grip bench - and I go very heavy with these - can only get 6 to 8 reps tops each set. This has personally resulted in great gains in size and strength for my triceps.
Biggest piece of advice, though, is keep switching things up!