Sri Lanka, chasing 208 for victory, had lost two early wickets after a double-strike from Aaron Cowley and were 51 for three at one stage.
Lakshan slammed a fine unbeaten 101 from 120 deliveries with the help of eight fours and one six.
Earlier in the day, Mendis had also grabbed three for 35 with his spin bowling to restrict Ireland to 206 for eight in the 48-over match after openers Jamie Grassi (75) and Mark Donegan (36) had provided their side with a 73-run start.
Lakshan later said that he had not been bothered by the fall of early wickets and praised his captain.
"I'm very happy that I got a hundred today.
I got a lot of support from our captain. When he walked in, our first target was to make sure we got close to the opposition total. We set small targets and achieved it", he said.
Captain Raynard van Tonder slammed 143 off 121 balls, smashing 14 fours and five sixes, and was associated in a 125-run second-wicket stand with left-handed opener Jiveshan Pillay (62 off 67 balls) as the team virtually batted the opposition out of the contest.
Kenya were never in the chase and eventually finished at 172 for seven in 50 overs after being reduced to 50 for four in the 19th over and then 98 for six in the 34th over.
Jasraj Kundi (41) and Ankit Hirani (35*) were the main run-getters for Kenya as the two put on 57 runs for the seventh wicket.
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