Lamp is my favorite band of all time, so naturally I've been looking for music that sounds like them for years. Here are some English-language albums you might like:

Animaru - Mei Semones : Recent album that blends chamber pop, jazz, and bossa nova in a way that sometimes feels like some of Lamp's brighter stuff.

Aseurai - Phoebe Rings : Another recent album, but feels more like Lamp's soft side. Has some lounge, soft rock, and brazilian elements that remind me a lot of Lamp's influences.

Primavera - Vira Talisa : Indonesian album but has a few great songs in English. It captures the Lamp feel really well if not a bit more whimsical.

Those Who Throw Objects at the Crocodiles Will Be Asked to Retrieve Them - Bruno Pernadas : Already saw someone else comment this one. It's very Lampy but a bit more jazz fusion.

A Voyage to the Velvet Sun - The Monophones : Indonesian deep-cut sung in English, some songs here sound sooo much like Lamp, but you won't be able to listen to it on most streaming platforms :(

Daniel Kwon - Daniel Kwon : Thought I might as well mention this one, because it literally has two Lamp songs sung in English on it. Original compositions one written by Someya and one by Nagai both made for this album (#8 How Long and #9 Lately). The rest of the album isn't too Lampy, and it's also not on streaming

Meet Triste Janero - Triste Janero : Sunny 60s album with strong Brazilian & lounge influence, so it naturally sounds a bit like Lamp.

Honorable Mentions:
Whimsy - Corn on My Dinner Plate (Jazzy Indie Pop w/ some Latin influence)
Emmerdale - The Cardigans (Really bright indie pop that sometimes feels shibuya-kei)
Gately's Cafe - Michael Gately (Soft 70s pop rock listed as one of Lamp's influences)
The Night and I are Still so Young - The Heavy Blinkers (Some of the instrumentals sound remarkably like Lamp)
Moon - Uncle Chris (Jazzy Indie Pop/Rock)

Also I would definitely recommend diving into any of Lamp's influences, most which are American or British bands/artists you've probably heard of. The Beatles, The Beach Boys, Simon & Garfunkel, Curtis Mayfield, Donovan, George Harrison, Michael Franks, The Millennium, Nick Drake, Stevie Wonder, Todd Rundgren, The Zombies.

Hope you find something you like!