Both red and white wine is produced on the island, the quality varies greatly from year to year and the small yields do not allow exports or even bottling it. Your best chance in trying some Lerosian wine and other alcoholic beverages of Leros is to go to the Wine Festival which is held in the month of August in Xerokampos.
I MUST warn you though! Some red Lerosian wine is not for the faint hearted, certain variety which is slightly sweet is refered to by myself and other Lerians as "KOUTELITIS" direct translation is "Hits you in the forhead" this wine is very pleasant to drink and you wont know otherwise untill after only a few glasses you are about to go home and the Lerian breeze hits you and promptly reminds you a simple fact: you are drank.... Oh I remember many a good nights.... ahem wait a minute... I meant... I can NOT remember many a good nights after a few glasses of a "Koutelitis"....
I will try and get some information on producers and were you can get some Lerosian wine if you are visiting other months but August.