Lindsay Lohan is fiercely determined to live alcohol free -- and toward that end she's ridding herself of ALL traces of booze ... everywhere she goes.

Lindsay vows to stay clear of the hard stuff and not just in her home.  We're told she will make demands that hotel rooms, dressing rooms ... even mama Dina's home is alcohol free when she's present.

Fact is ... so far so good.  Lindsay checked in to the Bev Hills Hotel this week and ordered the staff to remove alcohol from her room prior to her arrival.

Lindsay says she'll travel with a sober coach for at least the next week, to make sure she doesn't succumb to temptation.  Ditto when she guest hosted "Chelsea Lately" ... she insisted her dressing room be stocked ONLY with non-alcoholic drinks.