Convert urban/hybrid with hydraulic disk brakes from flat handlebars to drops
What you want to look for are hydraulic brakes for single-speed bikes. You can definitely get full sets including levers and calipers, I doubt you'll have luck finding levers that are compatible with the MTB calipers you have, check the manufacturers specs or get in contact with them directly to determine compatibility.

Not a recommendation, just an example, a little searching led me to TRP Hylex