Shimano have this v-brake levers in the product family DXR for BMX.
Is there any difference between a BMX brake lever and an MTB one? Are they smaller?
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Most BMX Levers are "Standard Pull", which means they have the shorter pull and are typically paired with road bike brakes (caliper, cantilever, mini-v, or road disc).
Mountain bike brakes (like v-brakes, or mtb disc) typically pair with "long pull" levers, which pull more cable. This is also known as "linear pull"
So, if you use a BMX lever with V-Brakes on a mountain bike, you likely won't be able to pull enough cable to work properly. You'll probably be able to stop somewhat, but they will feel off and will have to be setup so the pads are very close to the rim. You're better off getting MTB specific levers.
However, it appears that the Shimano DXR brakes and levers are linear pull, contrary to standard BMX tech, so it's likely fine to use this particular lever with v-brakes on a mountain bike.