The Louth and Horncastle MP met with a high-ranking Lloyds official last week.
It follows a decision to close branches in Coningsby, Alford and Mablethorpe in October.
Although Ms Atkins - and East Lindsey District Council leader Craig Leyland - were left frustrated, they did secure assurances from Lloyds.
They included a pledge that there are no plans to close town centre branches in Horncastle and Louth.
In addition, Lloyds have promised to help elderly and other vulnerable people cope.
Arrangements will include the provision of mobile banking in Coningsby, Alford and Mablethorpe.
Ms Atkins warned people needed to use high street branches, or risk more closures.
Ms Atkins said: “The talks went as well as could be hoped.
“Sadly, the decision has been made by Lloyds and they weren’t moving.
“Coun Leyland raised a number of concerns about the closures.
“Lloyds listened with interest and have set out the measures they are going to take to address those concerns.
“For example, we are going to have mobile banking units in all three sites - Coningsby, Alford and Mablethorpe.
“They will visit Coningsby once a week and Alford and Mablethorpe twice a week.
“I have asked them to look again at Coningsby to see if it needs to be twice a week.
“I am also asking for them to decide on the best time for the mobile service.”
Ms Atkins pointed out Lloyds customers can still access banking facilities at Post Offices.
She added: “I have been assured that vulnerable customers will be looked after.
“Also, for those customers who can make the transition to internet banking, Lloyds have assured me they will be give as much help and support as they can.
“We explained a lot of elderly people don’t use the internet. Local demographics mean we have an elderly population.
“In rural areas, transport is not as easy as it is in urban areas.
“That’s why I invited Lloyds here to show how difficult it is to get around.
“They have assured me they will take those access issues into account and if in a few months people are having problems getting to Horncastle or to Louth, we can look again at mobile banking.”
Regarding the town centre branches in Horncastle and Louth, Ms Atkins said: “We asked and they have said there are no plans (for more closures) but they can’t give any guarantees regarding the long-term.
“The basic message is a lot of people are using the internet for their banking - fair enough. If we want local branches we have got to use them.
“In Coningsby, Lloyds had 20 regular users a week. The figure is higher Alford and Mablethorpe, but still well below the national average.”