You can fruit both lychee and white sapote in lowland tropical conditions, but it works thanks to specially selected varieties. Here in Hilo there are specially selected lychee varieties that will flower and fruit without drought & cold stress provided they get pruned and fertilized right after harvest/during harvest and then are left alone, not fed again. White sapote do better upslope but they can easily be drought stressed in Puna next to the ocean in the lava where they can dry out during short dry spells. I've tasted delicious sea level grown white sapote up Hamakua as well, so I tend to agree with Oscar, they seem more adaptable than lychee, doing surprisingly well in super wet tropical microclimates like my own 200 inches per year rainforest climate.
Hawaii is 100% tropical, but unlike Puerto Vallarta and other continental-influenced locations, Hawaii has less temperature extremes, because Hawaii is surrounded by water. Luc's N=1 experiment is an example of the wrong variety for his location, however, it's not enough data to conclude that he couldn't fruit them there. But I don't blame him for not pursuing it further, so many tastier things to grow.
It's not true that Hawaii's "cooler" heat moderation makes it easier to grow highland crops. My place is at 500m elevation and frequent cloud cover and rain keeps us in the 68-80F range. Yet I have the same difficulty with highland crops as Floridians and folks at sea level have, I can't grow highland crops, lucuma won't grow for me but canistel thrives, lilikoi thrives but tacsonia passion vines die. Mountain papayas die, but regular papayas thrive. Cherimoya aren't happy at all here either. I stubbornly try to grow Andean palms but they croak here. I've killed dozens of ceroxylon palms. But some highland plants seem to adapt, for example, white sapote is an exception, same with tamarillos and I did find some lower elevation Vasconcellea that work as well. IMHO lowland tropical isn't defined by the presence of scorching temperatures, but by dew points above 16C and the absence of temperatures below 16C.