Morecambe town centre's branch is on a list of post offices earmarked for possible closure.
More than 1,000 staff across the UK could lose their jobs in a radical shake-up as the Post Office laid out plans to stabilise its finances.
The Communication Workers Union (CWU) representing Post Office staff has hit out at proposals, describing them as "immoral".
The Post Office is looking at options for the future of its business. One option is the closure of up to 115 branches, said to be loss-making, including the site at Victoria Street in Morecambe town centre.
Proposals aim to place postmasters at the heart of the government-owned business in the wake of the highly-publicised Horizon IT scandal.
This saw sub-postmasters wrongly jailed after faulty computer software made it appear as though money was missing from their accounts.
Their ongoing fight to secure redress and compensation was highlighted on the award-winning TV drama 'Mr Bates versus The Post Office'.
Alternative franchise arrangements could see an operator like WH Smith or another third party take on the branches.
In 2016, Lancaster's General Post Office on the corner of Meeting House Lane and Fenton Street closed down and services moved to WH Smith on Market Street.
"CWU members are victims of the Horizon scandal - and for them to now fear for their jobs ahead of Christmas is yet another cruel attack", said Dave Ward, general secretary of the CWU.
"While we are in the middle of a government review of the Post Office's future, the employer has embarked on its own strategic review.
"It seems the Post Office has learned no lessons from its chaotic and uncoordinated mistakes of the past.
"We call on the Post Office to immediately halt these planned closures and the attached consultations - which, historically, have been nothing but playing lip service - and engage with the CWU on protecting jobs and services.
"We also call on the government to intervene over this shambolic decision."
A strategic review of the Post Office business was called in May, by new chairman Nigel Railton.
He told staff on Wednesday that postmasters could expect up to £120m in additional remuneration by the end of the first year of the plan, representing a 30 per cent increase in revenue share.
This would tackle long-held complaints about poor rewards for postmasters' work, and there were also promises of lless red tape and a better voice in decision-making.
Mr Railton said: "The Post Office has a 360-year history of public service and today we want to secure that service for the future by learning from past mistakes and moving forward for the benefit of all postmasters. We can, and will, restore pride in working for a business with a legacy of service, rather than one of scandal.
"The value postmasters deliver in their communities must be reflected in their pockets, and this Transformation Plan provides a route to adding more than £250m annually to total postmaster remuneration by 2030, subject to government funding.
"It begins a new phase of partnership during which we will strengthen the postmaster voice in the day-to-day running and operations of the business, so they are represented from the frontline to the boardroom."
Kendal Post Office is also on the list of branches under threat.
A spokesperson for the Department for Business and Trade said: "The government is in active discussion with Nigel Railton on his plans to put postmasters at the centre of the organisation and strengthen the post office network for its long-term future."
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