The only AA lie-flats to Hawaii are from DFW to HNL or OGG. You could book separate tickets onto LIH on HA, but you will need to collect and re-check any bags. (Or pay the ridiculous price to include a HA segment/codeshare).
I think UA may have one lie-flat flight on LIH-SFO, but I’m sure it’s a regular seat from DFW to SFO.