https://www.planetf1.com/news/mattia-bi ... ap-record/
Rubens Barrichello currently holds the lap record in an F1 car at Mugello, setting a 1:18.704 in the Ferrari F2004 with a V10 engine, but already the two-year old Ferrari (SF71H) which was used in the private test this year was troubling that time.
“We did a very similar lap time with full tank, not pushing, et cetera. So I’m pretty curious to see when we set the pole, I’m pretty sure it will be a record,” he is quoted by Racefans.net.
The test itself was a private one, so I don't believe any lap times were recorded publicly, but say they were doing high 18's - mid 19's on full tanks of fuel, you'd imagine seeing times around the 1:14's in qualifying trim (if you're in a Mercedes
As for Ferrari having any advantage... I reckon they could spend a whole year with the SF1000, pumping lap after lap around Mugello, have absolutely everything optimised, setup perfectly, know exactly every square inch of the track and Mercedes would still pull a second on them after FP1.