I think that actually it's not the lottery that may "inspire" more people get the vaccine in Romania.
One additional "detail" is that those getting the vaccine in these last months of 2021 will also receive 100 RON (~20 EUR) tickets they can use in supermarkets (in theory, for food).
The hugely rising numbers of infected people filling all the news also did their part.

The number of newly vaccinated is rising from lows under 5000/day in August to 15-20000 (and rising) lately.