I too am a fan of QLab. A few years back, I worked on The Triumph of Love, a new adaptation by the director of the show. There were a lot of gags in the show, including a fountain of Eros that peed. As others have mentioned, the Sound Designer would give me CDs of new cues, and sometimes during production meetings, he would actually load the cues up into my laptop (there wasn't a house sound computer at the time) for me. Then I would run sound, as it was easier for me to hit the space bar than to ask my PA (no ASM required in Lort-C non rep) to do it, since she was busy tracking props.
For some reason, I've really never had trouble taking blocking and running sound during rehearsal. I think my training during my internship of taking line notes really helped me with having my hands, eyes and mind being several places at once. I wasn't one to keep my eyes in the book constantly: I would spot memorize, look up at my actors and be prepared to feed the line up to them, instead of burying my face in my script. Coming from years of working with actors who don't always say "line", it's been really important for me to look up at them for visual cues for them wanting me to give them line. And, after spot memorizing, feeding the line, I would immediately begin to write the line note down for them, while reading ahead and watching the next person for their potential line call. For me, this "3 places at once" feel has made it easy for me to read the script, watch the actors to take blocking, and have my other hand poised on the space bar to hit the next sound cue.
When it comes to editing the sound, I did as others have said: take notes into the rehearsal report for the designer. It was understood that I couldn't do everything the director wanted right away, and that hopefully tomorrow we would have what the director wanted. Though I will say, if the director told me "have this song start 20 seconds into the track" or "have this fade out after 20 seconds" I always opted to punch that into QLab right away, and then take the note for the designer in the report. For me having done that right then, I didn't have to take my eyes away from rehearsal, or watch the counter. QLab had it taken care of for me, and I could continue with rehearsal as usual.
I will say, going back to TOL, I had the most difficult time with my director regarding sound. We had worked together before, but this peeing fountain had become a rift between us. She required the sound of the fountain to only come out of the speaker on SL of the rehearsal hall. There was a back and forth play between the peeing fountain and Arelcchino who "played" the guitar on SR (actually a sound cue). She wanted it working now - so the best I could do "right now" was run the cues, but switch the faders on the sound board with my other hand. It wasn't the cleanest, and it broke up my ability to write blocking notes with my right hand. In an effort to make my own life easier for comedic moments like these (as there were plenty in the show) I had to spend my dinner break that day figuring out how to make the pee sound come out from just one speaker, while the guitar cue came out of another speaker, and then repeat what I'd figured out on all of the other fountain peeing cues.
Yes, I feel that particular situation should fall in the "I'm sorry, I don't know how to do that" category, but I am a sucker for making the director happy - and generally, in my personal experience, if the director is happy, my life is easier. Granted, I could've run the sound as it was, and switched the faders for that scene, but then I would've had blocking holes in my script, and that wasn't going to be acceptable. The show was moving to another theater after a month-long run at my theater, and I would be handing it off to a new SM team. And for comedic moments like this, there were full pages of hand written blocking that did not correspond to any text, and had to be inserted into the script as a new page, for a series of cues to be taken off of. I had to be precise and not miss a thing, so that the blocking for these moments could be as exact as possible.
Years later, I've found myself helping out a small theater company who has leaned heavily on my knowledge of QLab and treated me as the SM/Sound Designer. Granted, these are staged readings with 8-20 hours of rehearsal, a tech, one show and we're out of there. The pay is low, but the expectations aren't as high as a Lort theater. I will admit, I'm not a fan of doing it for a theater that is well-equipped and funded, but for the short gigs where it really is about the love of the book, I don't mind doing a little extra to make a reading extra special.