Weekend or weekday makes some difference, but not much. I don't worry at all about early morning traffic on the weekend. During the early morning, even during the week it's not that much of a worry.

This has to do with your stress tolerance. I'd rather give up a half hour of sleep even if I'm doing last call on the roof top lounge, than stress out about making my flight. For an 8:50 flight I'd personally calculate it this way.

The plane is supposed to board a half hour before departure time, so that's 8:20. I like to enjoy the lounge for about 30 minutes and the walk from lounge to gate can be ten minutes, so subtract 40 minutes. That means 7:40. Even on a bad day, with priority access FCO isn't LHR and you are usually airside in less than 15 minutes. That means you are down to 7:25. With no traffic and a good cab that shows up on time it's a 35 minute ride, so that means 6:50. I never check luggage so I have no experience with that, but with priority access I'd guess it can add up to 20 minutes, so that's 6:30.

Give yourself whatever cushion you're comfortable with, stress wise, for traffic and the unexpected. For me, that's usually about an extra 45 minutes. That means I'd ask for the cab to pick me up at 5:45 for an 8:50 flight. Barring some catastrophe that would get you there with enough time to spare and, to not stress over it, but somewhat sleep deprived. You can trim the 5:45 time up or down according to your stress tolerance about missing your flight. You can also delete the half hour in the lounge, that's just my custom.