Gerry Blaikie won the Bare seat with 428 votes, with James Andrew Sommerville (Green) second with 301 votes.
MBI candidate June Irene Ashworth was third with 243 votes, followed by Jane Wangui Cottam (Conservative) with 215 votes and Labour's Valerie Joyce Rogerson on 107 votes.
The by-election was held after the death in May aged 68 of Coun Stephie Barber, former leader of the Conservative group.
In the by-election for Upper Lune Valley, Ross Douglas Hunter won a seat on Lancaster City Council for Lib Dems with 390 votes.
In second place was Iain Scott Harbison (Conservative) with 183 votes, followed by Nicky Sharkey (Green) on 24 votes and Faith Kenrick (Labour) on 21 votes.
The by-election followed the passing of Coun Stewart Scothern, previously the Conservative representative for Upper Lune Valley, who died in October, aged 73.
The wins follow a double success for the Lib Dems in Morecambe Town Council by-elections last week.These results mean that the Liberal Democrats have now made seven gains since May in local by-elections, increasing their representation on Morecambe Town Council from one to six, and doubling their number of Lancaster City Council seats from two to four.
Coun Hunter said: “I am honoured that the people of Upper Lune Valley have put their trust in me. I am relishing the opportunity to work with the community in order to tackle the issues that have been identified in order to make the Upper Lune Valley an even better place to live in and enjoy.”
Coun Blaikie, Bare ward’s first ever Liberal Democrat councillor, said: “I am delighted that, after being elected to Morecambe Town Council in August, the residents have once more supported me to represent them, this time on the city council.
"The team and I have been out and about meeting the residents to discuss the issues that need addressing. We will be working in tandem with the community to take action.”
The local Liberal Democrat chairman Peter Jackson commented: “Something very special is happening in Lancaster, Morecambe, Heysham and the rural areas.
"These results mean that the Liberal Democrats have won seven by-elections in the area since May and it is clear that the other parties are being rejected by the residents in favour of a different, community-based way of doing politics.
"We are offering a genuine partnership between the community and councillors to tackle long standing issues which have been neglected for far too long. The residents are buying into this, and I invite anyone who wants to get involved to get in contact with us.”