Abysmal first-innings batting by the Red Rose county, who were dismissed for 92, left them relying on Lyon and English Test novice Tom Hartley spinning them to victory on a fourth-day pitch in Manchester.
But with Kent captain Daniel Bell-Drummond making an unbeaten 79 it was Victorian Wes Agar, who took seven wickets in the match, who was the man from Down Under on top.
Lyon took 2-48 in Kent's second innings, including a smart caught-and-bowled, but they were the only two wickets to fall on Monday morning as Kent chased down the victory target of 164 with few alarms.
Former England Test bat Joe Denly hit the winning runs as Kent left Lancs rooted to the foot of the ten-team County Championship, winless after four matches. Two teams are relegated and with 27 points Lancs are already 16 points adrift of the last place of safety.
Kent made 261 in their first knock (Lyon 3-50) enabling them to make Lancashire follow-on 169 behind. In their second dig Lancs did better, making 332 as Agar, who plays for South Australia at home, finished with match figures of 7-100.
With England Test opener Zak Crawley out late in Sunday's play Kent resumed on 1-71, still requiring 93. Batting positively against the turning ball Kent lost Ben Compton to a low return catch by Lyon for 29, then Jack Leaning caught slip off the Australian for 16.
But with Hartley lacking threat and too few runs to play with to set aggressive fields, Lancashire were unable to make any other inroads.
Lyon was originally signed for the duration of the English summer, in all competitions, but after Cricket Australia intervened, citing concern over his workload, that stint was cut to seven of the opening nine red-ball Championship matches.
Lancashire have three more such matches in May, then two in late June. In his four matches to date Lyon has taken 12 wickets at an average of 26.92.
15°C