But the most he earned was £15 a week and the striker, who played for Notts County, Arsenal and Chelsea, struggled financially after retiring in 1955.
Blues fan Lord Attenborough replied with a cheque of £100.
The letters went under the hammer at Nottingham-based International Autograph Auctions on Saturday.
Auctioneer Richard Davie called the correspondence “very poignant”.
Lawton had asked Lord Attenborough for £250 – about £3,700 in today’s market.
“This is a sad letter for me to write, Dickie, after so many years,” one letter from Lawton reads.
“Could you let me have a loan of £250 to be repaid in the course of 1 year. I would not ask if it wasn’t so urgent and lose your friendship, but all I need is time.
“Please, Dickie, please help me. If you cannot see your way to do so, don’t think too badly of me.”
The pair’s relationship went downhill when Lawton seemingly failed to pay Lord Attenborough £10 for two FA Cup tickets he provided in 1971.
The letters show Lawton – who Lord Attenborough called “the greatest centre forward” he had ever seen play for England – had later asked for help getting a job with singer Adam Faith, who had started a furnishing firm.