The Australians starred in Northamptonshire's third straight win which took them top of the Central and West Group.
James Sales took 5-21 to help restrict Gloucestershire to 9-164, with Ben Charlesworth striking three sixes in his 49.
But Lynn and McSweeney set about the visitors' attack in reply.
Lynn, who plays for Adelaide Strikers in the Big Bash League, struck five sixes in a 36-ball 69.
McSweeney, who plays for South Australia in the Shield and one-day Cup but for Brisbane Heat in the BBL, hit 53, clearing the ropes twice.
In Cardiff, Glamorgan beat Somerset by seven wickets for their first Blast win of the season.
Sydney Thunder star Nathan McAndrew produced his best with the ball, taking 4-15 to help reduce Somerset to 9-171.
Opener and skipper Kiran Carlson struck six sixes and 13 fours in his 109 off 45 balls as Glamorgan chased down the target inside 14 overs.
In other matches, Yorkshire maintained their 100 per cent start in the competition by beating overnight North Group leaders Durham by 58 runs at the Riverside.
Derbyshire beat Nottinghamshire by 23 runs, while Leicestershire sealed their first competition win of the season with a thrilling two-wicket defeat of Lancashire at Old Trafford.
Worcestershire beat Warwickshire by six wickets at New Road, the visitors still winless after slipping to a third straight defeat this season.
South Group leaders Surrey slipped to their first defeat, losing by five wickets to Hampshire in Southampton, while Essex scored a convincing nine-wicket win against Kent in Canterbury.
with AAP
9°C