First off, to echo @Pepepicks66, your takes sound great!
Warning, words ahead. I’m not known for my brevity
I typically try to approach things consistently, so, yeah, I mostly follow the same routine whether I’m learning something new or maintaining. Again, it depends on the complexity of the lick, the last time I played it, etc. Basically, if I’m learning something new I’ll slow it down to a reasonable speed so I can get the fingering down. Reasonable means slow enough to learn it but not too slow so that it’s not challenging. If a lick isn’t too difficult then slow might be 115 or so. If it’s intricate then slow might be 80. If you’ve been playing John Petrucci licks for the past 20 years then slow might be 140. It really just depends. Me, personally, I start at 80 and bump it up to whatever I need to. If I’m maintaining I usually will attempt to play the lick at speed or above, if it’s a lick I haven’t touched in a while I’ll start at speed and adjust from there. Once you have it, you have it, you just need to dust it off.
As far as time spent playing slow before I kick it into gear, I take as long as I need to get the lick into my head or as Paul Gilbert says, “to make it bulletproof”. I don’t usually speed up a lick until I have it down. For me, that time spent up front is invaluable. I know that’s not really an answer, but I don’t have a hard and fast number. On average? If it’s a semi-challenging lick then I’ll take a few days of multiple practice stints (15-20 min ea.) to get it down and then ramp the speed up to around performance level. At that point I then chunk it; I take parts and I focus on increasing the speed of them separately instead of attempting to shred the entire thing at once. Example, I recently worked a lot on the first part of JPs Gemini. It’s not a super-difficult lick, though the string-skips are murder to me, but it is JP so it’s played fast (143). I started playing it at 80 to simply learn it and did that for 3 or 4 days until I felt comfortable enough to start ramping it up to speed… which it still isn’t The point is that I try not to jump the gun and I take whatever time I need to learn a lick backwards and forwards before I attempt to push it. Again, speaking only for me. It takes me time to learn something new. It might not take other people nearly as long.
This is not to say that once I speed things up I don’t make mistakes. I do, most certainly. I think we all do (if I can say that). Isolate those parts, slow them down a little, make them more bulletproof, then ramp it up again. Eventually it’s going to come together. But I don’t think hammering away at it for an unrestricted length of time is a worthy endeavor because I think after a certain amount of time you’ll hit a wall and you won’t make any real progress.
I hope this helps!