The lifters per se are not particularly at risk. (This assumes no sliding fit limits are exceeded by the lifters in the lifter bores operating above some safe speed.)
The real risk to the engine is from the possibility of valve float at the elevated red line.
There is another risk. The engine's oiling system may not be capable of supplying air free oil at the higher RPMs. As a result the hydraulic lifters may partially collapse at higher engine speed and if this happens performance will fall off. There is the risk presented to critical main and rod bearings being supplied oil with air in it.
I would think 6600 rpm is a bit aggressive for a stock motor. I had my tune done by Sean Powell of Hemifever and he set my rev limiter to 6200. You don't say what motor you have, mine is the 5.7 w/6M and the torque peaks at around 4500 rpm if I remember correctly, and starts dropping off around 5200 so if you shift around 5500 you should be pulling the next gear around 4500, keeping the engine in the peak power curve. I don't think there's anything to gain going beyond 6000 rpm and it puts undue stress on the internals.
Of course, things are different with an automatic trans, but the power curve should be the same.
When I had my R/T I ran a Mopar TCM and the car would shift at 6,200 rpms under hard acceleration, I set my rev limiter to 6,600 and never had any problems. I don't think shifting the 5.7 at anything over 6,200 rpms will do you any good though as the motor isn't really building any more power at that point. After a good bit of experimenting at the track I decided (at least for me) the sweet spot seemed to be 6,200 rpms for drag racing.