Eranga finished with 4-49 and Lakmal claimed 3-66 to help bowl out Bangladesh for 232 after the tourists won the toss and elected to field at the Sher-e-Bangla stadium.
Skipper Mushfiqur Rahim (61) and Shakib Al Hasan (55) were the only batsmen to resist the accurate Sri Lankan attack on an even-paced pitch.
Sri Lanka made 60 for no loss in reply by stumps, with Dimuth Karunaratne unbeaten on 28 and Kaushal Silva on 30. They are now 172 runs behind with all 10 wickets in hand.
Shakib and Rahim joined hands at that stage to stitch together a fifth-wicket stand of 86, before the hosts suffered two quick blows to slip to 150-6 midway through the afternoon session.
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Shakib fell leg-before to veteran left-arm spinner Rangana Herath, before Eranga had new batsman Nasir Hossain caught behind in the next over to claim his third wicket in the innings.
Rahim then added 53 for the seventh wicket with all-rounder Sohag Gazi before he fell leg-before to Lakmal soon after the tea break.
Debutant opening batsman Shamsur Rahman smashed 33 of the first 59 runs with the help of seven boundaries, but failed to build on the fluent start in the morning session.