Already been mentioned but the The Wizard of Earthsea (Earthsea Cycle) by Ursula K. Le Guin is the only other fantasy that feels "similar" to the Lord of the Rings to me (admittedly I haven't read a ton of fantasy, but I've read a decent amount). I'm reading through the series for the first time, on book three right now, and it's just great. Feel like it does a nice job of defying my expectations of a "fantasy story" and Le Guin's writing is beautiful.

Also these books straddle the line between fantasy and sci-fi, but the Broken Earth Series by N. K. Jemisin are amazing and among my favorite books. Actually gave the series a reread after my most recent reread of LotR earlier this year, so I can vouch they are an excellent follow up! These ones have less of an obvious fantasy parallel to LotR but they're too good for me to not mention!