Because of board rules, I'll try and be judicious.
JRRT is a rather conservative Catholic. The LotR taps into a 19th century tradition of English anti-modernism (eg Carlyle, Ruskin, etc). The key idea of LotR is that if people honour their responsibilities and don't try to overturn the natural order (which governs relationships among higher powers, between humans and those powers, among humans, between humans and the natural world), there will be peace and flourishing. In some ways, it's the same basic idea as in Arthurian romance - when the rightful king is on the throne, and the grail has been restored, there will be no troubles. But JRRT adds the anti-modernism (Arthurian romance didn't need to be anti-modernist, having been written in the pre-modern era): Sauron and Saruman use machines and mass armies; the ruin of the Shire involves tearing up hedgerows, building modern buildings, turning the mill into a larger factory; etc.
(Unlike the 19th century conservatives, JRRT lived through the 20th century apogees of modernism - the World Wars, the Depression, etc - which no doubt affected his views and coloured the way he presented his particular anti-modernist vision.)
For a fairly well-known criticism of LotR that attacks (among other things) its conservatism, see Moorcock's
Epic Pooh. Unlike Moorcock, I'm a big fan of LotR and the Silmarillion, but I think his essay is interesting and I wouldn't say that I straightforwardly disagree with it.
REH and HPL are quite different from JRRT. They're not anti-modernist, for a start - the Conan stories, for instance (and despite their setting and trappings), are thematically ultra-modern, with the triumph of the individual will over social convention and historical order. Both REH and HPL have something of an obsession with race and "purity of blood" (in JRRT similar concerns are framed in terms of history and heritage, rather than biology). And both are irrationalists - that is, sceptical of the idea that human beings, through reason-governed social organisation, can successfully improve the human condition.