The reclusive Lim, the Southeast Asian city-state's eighth richest man with a fortune estimated at $1.6 billion by Forbes magazine, said he will also make a further 40 million pounds available for manager Roy Hodgson to purchase new players.
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Lim said in a statement that his cash offer, funded solely by his own wealth, would cover the club's debts estimated at 237 million pounds.
The rest would meet bank interest and 40 million pounds for working capital and other liabilities.
"My offer provides a firm financial platform from which the club can rebuild. Given the manner in which the sale process has been handled, I feel [Liverpool chairman] Martin [Broughton] and the board owe it to me, to the club, and to the supporters, to consider my offer," Lim said.
The offer, revised after an earlier bid of 300 million pounds, has been lodged with Broughton. It comes amid a battle in London's High Court to decide whether the club's much-hated American owners Tom Hicks and George Gillett can block the club's sale to NESV.
Liverpool's independent directors led by chairman Broughton had earlier agreed to sell the club to NESV, the owners of the Boston Red Sox baseball team, in a deal valued at 300 million pounds.
Lim, 57, a sports fan better known for his links to Manchester United, made his fortune through stockbroking and has interests in a range of industries including palm oil, fashion, logistics, food and beverage and healthcare.
His investment holdings include large stakes in Wilmar, the world's largest palm oil firm, and Singapore fashion retailer FJ Benjamin.
"I am committed to rebuild [Liverpool football] club so that it can soon regain its position at the pinnacle of English and European football, where it truly belongs. This is why I have stepped forward with this offer," he said.
Singapore, home to one of the world's busiest container ports, is known for its business-friendly environment and as a financial centre, especially for private wealth management.
It is also seeking to put its imprint on the global sports scene - for the past three years it has immaculately hosted the only night-time F1 Grand Prix.
The city of 5.1 million people are football-mad. The English Premier League is a huge draw on cable TV and there are scores of Liverpool fan clubs across the island.
Bitter rival Manchester United is also extremely popular, and Lim has exclusive rights to own and operate a chain of Manchester United-themed restaurants and bars in Asia.
FJ Benjamin, in which Lim is the second-largest shareholder, previously operated the Manchester United Theatre of Dreams stores in the city-state.
Lim describes himself as the son of a fishmonger who worked his way through school as a cabbie, waiter and cook. He made his fortune as a stockbroker and became a private investor in 1996. He keeps a relatively low profile and rarely gives media interviews.
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