Shares are being offered at a 94 per cent discount to Friday's close price - 1p, compared with 16.25p.
Investors seemed more encouraged than last week: Lonmin's share price climbed 12 per cent in mid-morning trading.
The cash will be used to secure a new $370m loan that will mature in May 2020, replacing $543m, which matures next year. The net proceeds will be used to "fund the implementation of the business plan", which Lonmin says will enable it to withstand continued weak platinum prices and restructure the business for future growth.
The South African producer, which borrowed millions during the commodities boom, has been urging shareholders to support all its resolutions - including this rights issue - warning that if they do not they face the possibility that the company would have to close and they would lose the entire value of their shareholding.
Brian Beamish, chairman of Lonmin, said: "In order to be able to deal effectively with the effects of a continuation of current low PGM prices, the board and management have developed the business plan with the aim to achieve positive cash flow after capital expenditure.
"The rights issue is expected to raise approximately $407m in gross proceeds and is designed to strengthen the group's balance sheet and allow the implementation of the business plan, whilst preserving the long-term value of the group. The board remains confident in the potential of the group, with its high-quality asset base and long-term mining rights, and in the medium to long term fundamentals of the PGM industry and is focused on preserving and enhancing value for all shareholders."
Last week, the firm warned it would have to stomach a $2bn impairment charge as it braces for a period of weaker platinum prices.
This is Lonmin's second rights issue in three years.
The board has received financial advice from Greenhill for the rights issue.