The budget supermarket chain says the proposals will allow them to stock and sell more products at the shop, which is on Kingsway in the town.
If approved, the plans would involve 32 of the store's 144 parking spaces being wiped out to make way for the extension.
The eastern access point to the car park would also be closed off, with driving customers diverted to an entrance on the opposite side.
Lidl said they hope to start work this summer and complete the job by the winter, if they get planning permission.
In a statement, the company said: "We are delighted to confirm that we have submitted planning for a refurbishment and extension of our store in Ossett.
"If granted, our plans will see an increase in the overall size of the store to serve the local community an even greater selection of products in a new modern supermarket.
"We look forward to receiving a decision and updating local residents in due course."
The plans represent something of a change of tack from Lidl. They were controversially given permission to knock down four neighbouring homes to expand the Ossett store's car park by 47 spaces in 2016.
The supermarket said then that the extra space was necessary to cope with rising customer numbers, though 284 people objected, with one leading campaigner describing the move as "atrocious".
Now five of the store's neighbours have objected to the latest proposals, citing the prospect of more traffic along Kingsway and the proposed position of an electrical substation, which they fear will cause excessive noise.
Writing on Wakefield Council's planning portal, one said: "We are extremely concerned about the relocation of the substation to be immediately adjacent to the residential properties on Kingsway.
"Substations emit noise constantly and are incredibly disruptive to residents during evening and night-time hours when ambient noise levels have dropped."
Another said: "As residents we struggle to pull out onto the road as it is, this problem will be exasperated with the new traffic changes.
"We already feel that the traffic problem on Kingsway near the Lidl store is an accident waiting to happen and has been for some time."
The proposals will be either approved or rejected by the council, though it is not yet known exactly when a decision might be made.
Local Democracy Reporting Service