Billings showed his class on a tricky pitch to make 89 from 101 balls, a new Lions best for the Kent wicketkeeper-batsman.
But other than Dawson, who continued his excellent all-round tour by making 48 in a fifth-wicket stand of 106 with Billings, the rest of the Lions batsmen struggled, leaving their bowlers with only 216 to defend.
Pakistan A all smiles, after completing a comeback from 2-0 down to win 50-over series 3-2 – as Lions did in T20 pic.twitter.com/Otfj0E2rnk
— England Cricket (@englandcricket) January 30, 2016
Ball did his best with figures of 8-2-17-1, Dawson collected two wickets, and Tom Curran took two in three balls in the 42nd over to conjur hopes of an unlikely victory late on.
But Zohaib Khan and Mohammed Hasan held their nerve to steer the Pakistanis to a three-wicket victory with 13 balls remaining.
It was a reversal of the T20 series between the teams before Christmas, in which the Lions came from 2-1 down to win 3-2 after a Super Over.