As played I think anywhere from 1/3 to 1/2 pot seems okay, maybe induce a raise from Jx?
I am range betting this flop. Solver will bet close to 100% of hands on this flop (this is the general rule for most K high flops in 4bet pots).
I think range betting somewhere between 15% pot and 25% pot is fine. Another philosophy would be to mix like 10% pot and 25% pot. 25% pot is mainly AA, JJ, KJ, AK, weaker Kx (your 4 bet bluffs which should be KTs-KQs) mixes 25% and 10%, and KK and QQ prefer 10%.
Most of your bluff part of range would use 25% pot.
A way to think about this is when we bet 10% pot with QQ, we can get called by worse, and KK protects that range. KK is also incentivized to bet small blocking the call range and unblocking bluffs. Another thing about this is that live players don't know how to react to 10% pot, so if you know this part of the game tree better than they do, they are bound to make mistakes.
Another interesting point about you hand is that when we are this deep from LJ facing SB 3bet, our main action from solver is to flat KK, not 4bet. Here is GTO Wizard's range for 200bb at 500NL rake for LJ vs SB:
In general, all of these factors should influence us a bit in favor of flatting KK:
1. We are in earlier positions, including LJ, especially given this game has a straddle.
2. We we close the action heads up,
3. We are in position against a SB or BB 3bet, and
4. We are very deep.