The hosts chased a target of 185 with 10 balls to spare as Tom Lammonby (47 not out) and Will Smeed (44) also made impressive contributions.
Lancashire’s 184 for nine proved to be an under-par effort after they made a fast start in the powerplay.
Roelof van der Merwe (4/27) took crucial wickets at the top of the order despite 42 from Dane Vilas.
Somerset will join fellow South Group qualifiers Sussex Sharks and Hampshire Hawks at Finals Day on September 18 at Edgbaston.
One-time T20 winners Somerset will now hope to chase two trophies in September as they also go in search of a first County Championship title when the second phase of that competition begins on Monday.
Lancashire Lightning: 184/9 in 20 overs (Vilas 42, Jones 38 n.o, Van der Merwe 4/27, De Lange 3/41)
Somerset: 185/3 in 18.2 overs (Abell 78 n.o, Lammonby 47 n.o, Smeed 44, Lamb 2/24).