In return, pubs could ensure that they housed vital community services such as post offices or the local village shop, he said.
"By giving community pubs a small grant we can help keep rural pubs going and bring back vital community services.
"I want to see the County Council back this scheme and commit to supporting rural areas. I hope they will join me and back the scheme."
Research done by the Campaign for Real Ale (CAMRA) shows that two pubs are closing every day. Rural areas are particularly vulnerable.
Mr Farron suggested Cumbria could follow Essex County Council, which has offered grants to pubs of 50% of any capital investment, up to £5,000.
Local pubs could follow the lead of the Black Swan in Ravenstonedale – one of 354 pubs and small hotels helped by the Pub is the Hub charity, he said.
Ravenstonedale residents had to make a 12-mile round trip to their nearest shop until landlady Louise Dinnes started selling newspapers and groceries.
Pub is the Hub encourages local authorities, communities and licensees to work together to support, retain and locate services within rural pubs.
A recent poll found people living in rural communities were happier and better off if their pub offered more than food and drink.
Cumbria County Council leader Eddie Martin said the local authority had worked in the past to encourage pubs to help provide access to local services.
But the current financial climate meant it extremely unlikely similar initiatives would be viable, he told the North-West Evening Mail.
"It is unfortunate, but an economic reality and it seems an odd time for anyone to be calling for extra money to be found, given the scale of the funding cutbacks local government is having to deal with.
"The county council therefore focuses its efforts on providing access to local services through facilities such as libraries and Local Links."