Sussex made a superb start against Somerset with home openers Archie Vaughan and Lammonby falling to left-armer Sean Hunt for ducks.
They were 82-5 after Henry Crocombe removed the Rew brothers, James and Thomas, for 29 and 30 respectively, but Thomas hit 50 off 58 balls as he and Hill added 59 for the sixth wicket.
Thomas was caught behind off Hunt (3-35) but Hill (55) brought up his second successive 50, this one from 62 balls, and put on 67 with Kian Roberts (29) before Somerset were bowled out midway through the 48th over.
Tom Haines went early for Sussex, but they reached 60 before Lammonby had Charlie Tear caught at cover and won lbw decisions against Fynn Hudson-Prentice and John Simpson in the same over with inswinging deliveries.
Tom Clark (34) followed in the next, caught at mid-on from a leading edge, and although Jack Carson weighed in with 35 off 34 balls, wickets continued to fall as Sussex slumped to their third defeat.
“After getting out third ball for a duck I wasn’t really expecting too much from the day. But I got the opportunity to get a few overs with a new-ish ball. It swung around early doors which helped me,” said Lammonby.
“I got lucky with the first one and then I found my rhythm a little bit more. I was very pleased to pick up my first five-for. It’s a pretty cool and pretty special moment.”
The win lifted Somerset above Middlesex into second place, on the same number of points as leaders Yorkshire, while Sussex are sixth, four points behind the top three with two to play.
