One can do a messy but a "no removal of anything" cleaning and lubing while leaving all in place. Spray solvents, compressed air, spray lube, thick oil and rags are all you really need. Being able to rotate the bike so the levers are at the bottom helps with the cleanliness.

But I prefer to remove the shift/brake blades and shifter pod unit which does require removing cables, tiny set screws, springs and bushings. Once removed from the lever body the blades/pod unit can be soaked, air blasted and relubed without contaminating the bar tape. I'll generally replace the rear inner cables (both gear and brake) and rotate the old rear brake cable to the front, tossing the old rear gear inner.

I've done a lot of these shifter refreshens and there are a few series and issues that cleaning won't fix. But cleaning and lubing is so easy that it's worth it to try that first. Sorry I don't have a vid to link to there are way too many to screen. Andy