While you're practicing your speed you should also be paying attention to your muting techniques.
Playing fast is great, but if you keep leaving open strings ringing on it'll just sound sloppy.
Work slowly first and find out the cleanest and most efficient way to play the lick. When you have it down absolutely clean at a slow speed, then try gradually speeding it up over time.
The goal is to get to the point where you can play a lick subconsciously without even thinking about it .
Kinda like driving a car. When you first learn to drive all you can think about is what to do next....signal, brake, shift...
After a couple of years you can drive 20 miles past your own house and not even realize you were driving because you were thinking about something else.
Same thing with guitar. Get licks to the point where you can be thinking about what to have for lunch at the same time as you're playing.