Left hand, for lead:
1. Only fret the string you’re playing. When the note is done, you’re finger is off the string, exactly the opposite of chording.
2. Get used to using the edge of your fretting finger to lightly touch the edge of the next thicker string, wherever possible (less possible on sweeps and stuff)
3. Use the fleshy parts of the remaining fingers to lightly lay across the thinner strings.
4. NONE of these is perfect, and all have their limitations which is why you do each whenever possible and mix with…
Right hand:
1. Pinky is great for touching thinner strings lightly at the bridge. Some use the pinky as an “anchor” on the edge of the bridge or bridge pickup, or high E string
2. Use the part of your hand you use for CHUGGA CHUGGA riffs to mute everything thicker than the string you’re playing.
3.None of THESE are perfect, either, which is why you do each whenever possible and mix with right hand techniques.