I don't very much like the standard races conceptually - or rather I like only elves (and tieflings, but they aren't part of OSR). But I don't like those flighty wood elves, frolicking in moonlight, singing and dancing for all eternity. That's boring and not weird. On the other hand, I like the Lotfp concept of the nearly unkillable dwarf with lots of hit points. For the halflings, I have absolutely no use. Even if they have the best saving throws in the whole game. Stop! I have just re-read the halfling class in Lotfp. Suddenly I find intriguing things: they have +1 bonus to their Dexterity modifier, are very stealthy and even gain a +1 bonus to AC when not surprised. So I guess, I'll keep the class around.
That leaves me with two options: divest race from class (which is not at all supported by Lotfp) or re-skin them. Leave the mechanics intact, but put them in a different make-up or put a different spin on them. The goal here: make the classes weird. Even weirder than in Lotfp.
Dwarves - Sailors in Ships of Stone
The dwarves are hardy (as mentioned above). I like that. I want to keep them around. But hard-working dwarves living in subterranean fortresses - not weird! Dwarves loving the sea and roaming the waves in their galleys of stone are different. So the dwarves are a sea-going people, who live on huge galleys made from stone. The secret of fashioning them now lost to time. On the other hand, a stone galley just wrecks your average wooden ship. They are the rulers of the waves, caught up in commerce and piracy. Yet, still a dwindling race. Ruleswise they stay as they are.
Elves become Tieflings - Spawn of the Netherworld
The elves in Lotfp are rather strange. They are aligned with chaos. They are vulnerable to holy water and holy symbols. Also, some spells specify that elves are immune to them. You could easily use the elves as presented in Lotfp to model Melnibonéans or other extra-planar creatures. I love tieflings. Therefore, I am reskinning elves as tieflings. Mechanics-wise it is not a complete match, but close enough. Tieflings will have small horns (not like those huge horns of the type IV tiefling) and faintly smell of brimstone or sulphur.
Halflings become Marsh Elves - Dwellers beyond the Drowning Woods
My rpg experience is heavily influences by the fighting fantasy gamebooks (and especially the Sorcery! epic). In "The Seven Serpents" you meet these shifty gypsy black elves. In "From the Pit", you find out that they split from the Dark Elves, because they didn't like their evil ways. Now they are ostracized from good and evil elven society. I just like the concept: a broken elven people condemned to roam the country side having lost much of their heritage. I've already re-purposed the elves, so the halflings remain. Let's make the medium sized, leave all of the other stuff in place and transform them into wretched Marsh Elves. They are chaotic and all the rules about elves regarding holy water/symbols and spell descriptions apply to them.
Beyond the Drowning Woods there is also one important rule (taken from Swords & Wizardry): NPC members of the dwarves, tieflings or marsh elves may have completely different capabilities than the PCs.