'unknown ' lover as in its a secret. There may be future consequences sure (but maybe not now, with the Queen basically taking him under her), but who exactly at that point when it happened was going to do anything. He was kingsguard, so none of the other kingsguard would do anything. The King and Queen were not going to do anything. Corlys would certainly not do anything, he probably was happy to see him gone.
King regent to be would be the most pissed off but he cant do anything other then say hes a friend and i want him punished.
I think they both misread the situation.It might have been playful, but cole probably took it as a threat (when it was an attempt at being smug and playful given their shared secrets, and a way of saying im the same as you)
Cole probably just snapped and wanted it all to be done (given he was on his way to taking himself out).