Mr Lamont said that there is now no guarantee that the money given to Police Scotland by councils and private firms, over £9.3m in 2013/14, will be spent in the area that the money came from.
Figures from Police Scotland have shown that Scottish Borders Council will fund the equivalent of four full time equivalent police officers this financial year - £160,211.
However Mr Lamont has said that the City of Edinburgh Council’s decision to withdraw their funding could see others follow suit.
Mr Lamont said: “The money provided by councils and private firms helps to employ hundreds of officers throughout Scotland, but this funding is now coming under threat.
“Under the new single police force there is no guarantee that the money being spent will lead to better policing in the area the money came from.
“That is why Edinburgh council have withdrawn millions of pounds in funding, and it will not be long before others join them.
“Scottish Borders Council currently employs the equivalent of four officers region, but they now have no guarantee that they will be deployed in our region.”
Mr Lamont added: “Without this guarantee it will undoubtedly lead to questions over whether we should continue to provide funding.
“We need the best policing force possible for the region, but this money could be spent in other areas where we could guarantee a benefit to Borders residents.
“Police Scotland need to start providing assurances that the money we are giving them will go towards fighting crime in our region.
“If not, we risk seeing other councils withdraw their funding and frontline policing will take a huge hit.”
However, Scottish Borders Council’s executive member for community safety said that agreements are in place between the council and Police Scotland.
Councillor Donald Moffat, said: “Scottish Borders Council has service level agreements in place with Police Scotland regarding the deployment of funded officers, and is satisfied that these officers are undertaking duties in compliance with these and are deployed within the Scottish Borders.
“These officers undertake specialist duties to ensure that the Borders remains one of the safest places to live, work or visit within Scotland.”
The new single police force was formed in April 2013, with the Borders now part of the Lothians and Scottish Borders Division.