The phrase "attempt to lay a" is correct and usable in written English.
It can be used when discussing efforts to establish, create, or set something in place, often in a metaphorical sense.
Example: "The team made an attempt to lay a solid foundation for the new project during the initial planning phase."
Alternatives: "try to establish a" or "make an effort to set a".
The press and public had closely followed the attempt to lay a transatlantic cable, and reacted with enthusiasm when word of its success was reported.
On May 16, 1857, Harper's Weekly featured a cartoon about the first attempt to lay a transatlantic telegraph cable.
George Osborne bringing forward a bill to sanction the cuts in welfare benefits set out in the autumn statement is a crude, cynical attempt to lay a trap for Labour.
In a later conversation among the killers, one can be heard complaining about having to wear their victim's clothes, in an attempt to lay a false trail for investigators following Khashoggi's disappearance.
Partly in an attempt to lay a ghost to rest, partly to nourish her own difficult relationship with her father and partly because, let's face it, novelists (myself included) are always suckers for family secrets, Berne sets out to see what can be found of her grandmother.
To watch the outraged commentators attempting to lay a glove on him is to imagine them doggy-paddling in the wake of his best freestyle time.
When I attempted to lay a pink triangle wreath at Sachsenhausen concentration camp, in memory of the gay men killed there, I was stopped.
Field persevered for 12 years and through four failed attempts to lay a working telegraph cable across the Atlantic before succeeding in 1866.
British and American naval ships were instrumental in conducting hydrographic surveys in support of the early attempts to lay a transatlantic cable; the first successful cable was laid in 1866.
In 1905 (and again from 1918) Hilbert attempted to lay a firm foundation for mathematics by proving consistency that is, that finite steps of reasoning in logic could not lead to a contradiction.
