Livingstone was suffering with cramp in his calves but helped the tourists struggle to 217.
Ben Duckett made 59 and Joe Clarke 26 as only three England players reached double figures.
Bad light and rain halted Sri Lanka A's response but they easily reached their revised target of 201 without loss.
Sri Lanka A now lead the series 2-0.
Liam Livingstone's 94 could not prevent England Lions losing the second game in a five-match one-day series against Sri Lanka A in Dambulla.