They fear a proposed reduction in opening hours of the customer access point (CAP) located in Horncastle Library will affect the most vulnerable people in the area.
A campaign to highlight the problems that council cuts will cause has resulted in hundreds of supporters signing a petition to stop the reductions going ahead.
Bill Anderson launched the petition and said: “This is a very strange proposal, coming from servants of the community, who propose measures which would knowingly and adversely affect the most vulnerable members of our community, particularly the elderly, the hard of hearing and those who struggle with reading and writing, using the telephone or completing and understanding forms.
“Is this a sign of a caring council?”
ELDC states that footfall has dropped at Horncastle CAP since 2013-14, and suggests that more people are using the internet and phone.
However, Mr Anderson claims footfall has dropped because it coincides with a cut in opening hours at the library.
Mr Anderson also questioned ELDC claims that more people were using the internet and phones to contact them.
He says figures used by the council to justify the proposed changes are based on a 2015 survey which 360 residents out of a population of 136,000 responded to.
Mr Anderson pointed out that many people do not have access to a computer.
As well as reducing the hours at Horncastle CAP, ELDC is planning to cut or shut nearby access points at Woodhall Spa, Tattershall, Alford and Spilsby.
One of the options being put forward by ELDC would result in Horncastle being the only CAP open on Thursdays, serving the whole of East Lindsey District Council area.
Mr Anderson added: “How will Horncastle CAP cope with the influx of people wanting to see someone face to face?”
A spokesman for ELDC said: “The expectations of our customers are changing as is the way they access services.
“Whilst we recognise there is still a need for CAPs in some locations, customer feedback so far is telling us residents wish to do more over the telephone and online.
“It makes sense to consider shifting resources in that direction, whilst also being able to deliver a significant saving for taxpayers.”
Consultation about cuts to CAP opening hours throughout ELDC ends next week.