If the strength/intensity of the lightsaber blade remains constant but the material being cut becomes thicker or higher density then one would need to apply more pressure in order to continue cutting at the same speed. Otherwise the cutting process becomes slower.
This is appears to be what happened when Qui-Gon Jinn was cutting the door in The Phantom Menace. At first it was a single door so he was cutting a shallow circle with relative ease.
However the Viceroy then had the additional blast doors closed as well which greatly increased the amount of material the blade had to cut though. Qui-Gon realized this and abandoned the wide, shallow circle he'd been cutting, opting instead for a deeper and slower cut since there are 1) more doors to cut through and 2) the blast doors are likely made of some kind of higher density material.
So, per the films, it seems that when using a lightsaber the effort needed to cut something varies depending on the amount and density of the matter being cut.