lay (something) under (someone or something)
To place or drape something beneath someone or something. Please be sure to lay a tarpaulin under the space where you will be painting. She laid a placemat under the child's plate so food wouldn't get on the table.
lay something under something
to place something beneath something. Please lay a cloth under your workbench to catch the sawdust. Would you mind laying a sheet of plastic over the table?