We should fold our missed flush draw on the river; raising into a range that just completed its draws is a massive mistake.
We have a massive range advantage here. A small sizing (25% pot) is preferred to keep their wide range in while we realize equity with our nut flush draw.
Note: Sizing up to half-pot is unnecessary; a smaller bet achieves the same fold equity while protecting our stack depth.
When LJ leads into us for a small sizing, we have a trivial call. We are getting 5:1 and have the nut flush draw, which has plenty of equity to continue.
Raising the river is a significant error. Our flush draw missed, and the 6h completed the backdoor heart flush, which LJ has more of than we do.
Note: Raising a missed draw into a range that just improved is a high-variance play that loses to almost all of Villain's calling range.