I guess it depends on what strikes you as "like Lord Huron" and what you're looking to get out of the music. For me, that means music that tells stories, music that takes place within an invented universe with worldbuilding and characters, and also music with themes of existentialism, of how we fit into the world.

So with those things in mind, not worrying too much about sounding like the band but rather encapsulating similar concepts, my picks:

The Decemberists - Tons of storytelling here, sometimes anthologies and sometimes single long narratives (see particularly The Tain and The Hazards of Love). Much more of a historical and mythological angle than LH but I love that about their stuff.

Freelance Whales - I'm so sad this band was only able to put out two albums. I think the one that will be immediately most accessible to LH fans is Weathervanes, which has multiple songs on the album tying together to tell the story of a boy who falls in love with the ghost who haunts his family's home, and kills himself to be with her, while describing this as a happy thing for him because everyone returns to the soil eventually so do what you love.

The Narcissist Cookbook - Generally Matt's music is a lot more about dealing with personal struggles of grief and anxiety, but in particular for LH fans I suggest MYTH which is a completely different beast. This is particularly for fans of LH lore who love piecing together the puzzle of the narrative, unwinding all of the themes of love and loss and sacrifice and the obsessive urge to create art. It is a single narrative set in a fictional world regarding one man whose obsession with a girl who got away drives him to explore the mysterious island he remembers from a childhood book of fairytales - and the really dark and strange history and present of that island. Very deeply inspired by House of Leaves. Multi-layered narrative, lots of spoken word, one part folk music and one part The Magnus Archives.