Egdon Resources submitted plans to extend the time it spends drilling for oil in both Biscathorpe and North Kelsey.
The firm is seeking planning permission to extend the end date for its operations by three years.
Lincolnshire county councillors will make a decision on the applications at a planning committee meeting on May 14.
An application to explore for hydrocarbons at the site in Louth was approved in March 2015.
However, production work expired on February 28, 2018.
Since being given planning permission, Egdon said that low crude oil prices and delays in production at another well site have prevented the completion of the work.
Now, if given permission, the company’s remit at the site will last until February 2021.
Councillors will also hear an application for a site in North Kelsey which was deferred from a previous meeting.
Members of county council’s planning committee delayed a decision for the Egdon to continue drilling at the site off Smithfield Road for another three years.
Again, Egdon blamed low petrol prices and changing of licences for its failure to complete the work.
Mark Abbott, managing director at Egdon, said: “Planning permission was granted for the site at Biscathorpe in 2015.
“However the fall in the price of crude oil from $120 per barrel in 2014 to less than $30 in 2016 had a significant effect upon the commercial viability of drilling for new reserves.
“More recently, the price of oil has risen to $70 per barrel, making exploration more viable.
“Egdon is therefore seeking to extend the permission for a further three years to complete the construction of the wellsite, drill the borehole and carry out production testing.”
The council’s planning officer recommended granting permission for the application.
Egdon is also expected to re-submit an application to drill for oil and gas in Wressle, North Lincolnshire.
It comes after North Lincolnshire Council’s planning committee twice rejected proposals for drilling in the region.
The government’s planning inspectorate also turned down the plans on appeal but upheld a decision for the firm to retain the well at Wressle.