Reddit mentions of The Lord of the Rings

Okay here are some good options:

4-volume 60th Anniversary Hardcover Set

Harper, ISBN 9780007581146

Amazon Link

This set uses Tolkien's original dust jacket designs, the companion volume is great for those interested (they're basically footnotes in a separate volume) and the smaller volumes are more comfortable than single volumes.

Single-volume 60th Anniversary Hardcover

Harper, ISBN 9780007525546

Amazon Link

This lacks the companion but has Alan Lee's artwork (the guy who did the concept art for the movies) - personally I'm not a fan of the slipcase but depending on your tastes it can look great.

Single-volume Deluxe Edition Hardcover

Harper, ISBN 9780007182367

Amazon Link

Fancy slipcase, some illustration, not as good as they used to be (they moved manufacturing to China at some point iirc) but still a good option.

Single-volume 50th Anniversary Hardcover

Harper, ISBN 9780261103207

Amazon Link

Older but some prefer the looks of this edition, this one's the first to have the corrected text iirc.

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All of the above feature the latest corrected texts, and generally the difference between versions aren't great anyway - so your decision should be based on what kind of aesthetic/budget/supplemental materials that you want.

I would however specifically recommend the 4-volume set (or the B-Format paperbacks) if your brother's going to collect the other titles too (Silmarillion, The Hobbit, the Christopher Restrorations) since those are the most complete format/trim with most titles available.

This is probably the closest you'll get to original covers in a box set. They're stylized black-themed versions of Tolkien's personal artistry (compare this with this). I have them, they're quite nice. They're matte, not glossy, so they have a nice texture; and the binding is good so the spine doesn't crack if you set it down while open.

Unfortunately if I'm correct I believe your Sil/UT/CoH box set is Harpercollins, so you're probably in Europe or Canada. The ones I posted are published by Mariner, a division of Houghton Mifflin, for sale in the US. This looks like a somewhat comparable Harpercollins edition but I can't vouch for their quality and the covers don't appear to be accurate.

Digging a bit deeper into the Harpercollins library, here's a UK (IDK if you're in the UK but it's probably avaliable in other non-US distribution areas) Hobbit edition that looks just like the original. Here's a LOTR one-volume edition with a cover based on Tolkien's original design for Fellowship of the Ring. This looks like a pretty accurate LOTR+Hobbit paperback set, but it appears to not be in print anymore so you have to buy used or pay through the nose to get it.

Album of all the original covers for reference if you care