9:58 AM PT -- The CEO of Memory Lane tells TMZ, "Memory Lane Music takes pride in maintaining a positive relationship with all of our clients. We have not yet seen the lawsuit in question but it is our policy not to comment on ongoing litigation."

The family of the guy who wrote "Santa Claus Is Coming to Town" says they've been getting nothing but lumps of coal, when they should've been cashing in big on the holiday classic.

The tune was written by Haven Gillespie way back in the 1930s. Haven's been dead since 1975, but his family says it entrusted Memory Lane Music Group to continue collecting royalties on Gillespie's catalog. He also wrote, "You Go to My Head" and "That Lucky Old Sun" ... but they know the real money maker is 'Santa Claus.'

In a new lawsuit, obtained by TMZ, Gillespie's fam says Memory Lane is supposed to send them checks for 85 percent of all royalties, while the co. keeps 15 percent. The family says it met with Memory Lane's honcho in April, and he copped to having been very naughty for the last 2 years.

They claim he admitted stealing, so ... go ahead and check that twice, Santa.

According to the docs, the thievery cost Gillespie's heirs more than $700k -- and they're suing to get back the cash.