Where did you find information on Raki distilleries on Lemnos? I think you may be a bit confused. Rakii (Tsipouro) is Greek 'moonshine'. Not to be confused with Turkish Raki which is made and bottled commercially as Ouzo is in Greece. Rakii is generally made by individual families for their own consumption. There may be a place they share for the making of it but it isn't a 'distillery' in the commercial sense. If you wanted Rakii in a bottle from a commercial distillery, you would actually have better chance much nearer to your home.
https://www.forbes.com/sites/warrenb.../#49e09a251a81

If you got the idea from this description of a distiller in the village of Saint Sofia on Lemnos, read carefully. It says, " dwellers of neighboring villages go in turn and distil their raki. If you find someone there, he may offer you a tot of raki." Saint Sofia - Tourist guide of Lemnos and Agios Efstratios It isn't a commercial distillery.

In March, not even the most popular tourist islands are 'all that touristy'. In fact, they are downright dead as far as tourism is concerned. So as a reason to choose Lemnos, that really doesn't make any sense. You could choose any Greek island in March and be lucky if you saw more than one or two other tourists.

Regarding the one of only 2 deserts in Europe, that is also misleading. There is a small area of sand dunes that are indeed worth seeing but that hardly makes it one of only 2 deserts in Europe. That's a bit of a tourism marketing stretch. A desert by definition is anywhere with less than 10 inches or rain annually and sparse vegetation. So yes there is a desert area but it is not 1 of only 2 in Europe. In fact, some people argue whether there is any true desert in Europe at all or what area is a desert and which isn't or which is the 'only' real desert in Europe.
What is the largest desert in Europe?

With only 4 days/nights I would not move regardless of where you choose to go.