More likely that in sucking fingers they have bloated with gas/air in their stomach, my lambs are handled by me mainly but others do handle them and they are fine, although I don't let them suck on fingers...
In response to the main question I'd say either bloat or clostridial disease will cause sudden death, bloat more so... I lost a 5 wk old lamb this year just about to be weaned off milk, the time period between being fine and healthy to dead was less than 2 hours. If you keep losing lambs though I'd suggest finding another farmer, a lot of it depends on the start they have had in life. Vaccinate the others with heptavac asap.