"this lays" is not a correct and usable phrase in written English.
We would instead say "this lies." For example, "This book lies on the shelf."
This lays ground for what follows.
"But I think this lays that question to rest".
This lays bare, I think, a fairly mature sense of perspective.
"This lays a solid foundation for growth into the long term".
This lays the groundwork for a smaller next generation and increased family resources also go to educating both girls and boys for longer periods.
This lays down MDMA as it grows, and thus provides a record of exposure that is more reliable than users' own recollections.
This lays them open to especially damaging lawsuits from investors in assets affected by the rate-rigging, lawyers say, thanks to a quirk of American law.
This lays a shaky etymological basis for trance music, which was first cited in The Guardian in 1970 about shamanist tribal music played in Ethiopia.
Critics of rap and R&B often miss the intricate storytelling involved, but this lays it bare, and makes it look easy.
This lays down that no events, such as public dances, may be held on a Sunday if charges are made for admission.
This lays to rest, with a satisfying finality, the ghost of vitalism – the spooky, whiffy doctrine that there is some essence of life not captured by "reductionist" biochemistry.
