The all-cash offer of 115p a share is at a 26 per cent premium to the company's share price two months ago, before Promethean first announced that it had bought a 3.7 per cent stake in the bank.
However, shares in LSB, which specialises in providing loans to customers with poor credit histories, have crept up over the past few weeks on the back of bid rumours, and were already trading at 113.5p by the time yesterday's announcement was made.
Rumours of a counter-bid from the US private-equity group Steel Partners, at as high as 135p a share, were already starting to circulate yesterday morning, pushing the stock to 118.5p. Like Promethean, Steel Partners has built up a stake of about 4 per cent in the bank over the past few months. However, shares in LSB closed down more than 1 per cent at 112p.
In a short statement yesterday, LSB said it would consider the offer, calling on shareholders to "take no action in respect of Promethean's approach" in the meantime.
Promethean said it would not press ahead with a formal bid for the group until it had been granted access to the company's books for at least six weeks. It added that if shareholders preferred, it was willing to consider introducing a shares element to its offer.
LSB has struggled in recent months after an increase in bad debts drove it to a 22 per cent fall in profits last year. It also has the uncertainty of a Competition Commission inquiry into the doorstep lending market hanging over it. The commission has already said there is an unhealthy lack of competition in the market and it is expected to recommend changes to the industry regulations when it produces its final report later this year.
However, Promethean believes there is significant unrealised value in the company. At its interim results three weeks ago, Sir Peter said he believed LSB had "scope for much improved future performance".
If successful, the acquisition will be Promethean's first major purchase. Since floating on AIM in June, it has made only two small purchases.
In November, it took a 15 per cent stake in the home furnishings company Walter Greenback, and it splashed out £23.5m on the purchase of the consumer data supplier Data Locator last month.