What is a lençareja (medieval Spanish)?

I'm assuming the 1438 document you're reading is Corbacho by Alfonso Martínez de Toledo. The only references I can find to that term are from that work, and it seems that the meaning is not entirely clear to modern scholarship. There's a University of California Press edition under the title "Little Sermons on Sin", translated by Lesley Byrd Simpson, with an explanatory note on p. 199:

6. Lençareja or lencereja, to judge by the context, was a simple garment or headdress, probably of linen (lienzo). I have rendered it by "linen kerchief."

This does make sense in the original context, which describes a woman who shines like the stars even when made up with nothing more than river water and wearing a "lencereja". It's evidently something plain and common. Beyond that, we can only guess.