Malcolm LaVergne -- O.J.'s longtime lawyer and now executor of his estate -- sent a letter, dated April 25, to lawyers for the Brown and Goldman families regarding their civil judgments against O.J. ... and inviting them to a meeting this month to discuss their probate claims against the estate.

Among the topics LaVergne says he wants to share with Nicole Brown and Ron Goldman's families -- O.J.'s living revocable trust, his last 2 years of federal tax returns, federal tax liens, cash and jewelry LaVergne took from O.J.'s house after he died and videos he shot of Simpson's residence.

LaVergne says his goal is to be transparent with the families about the probate process, not necessarily to give the 1997 judgment against O.J. any special priority.

He points out, all claims against the estate have to be dealt with according to Nevada probate law.

He's aware 2 judgments -- one for Ron's dad and one for his mom Sharon -- are active in Nevada, but he says he can't find evidence of an active judgment from Nicole Brown Simpson's estate.

While he says he'd welcome any proof one exists, he's quick to add he has no intent to honor a judgment that's no longer active.

LaVergne says he's hoping to hold the meeting on or before May 10 ... but, adds any day in May all the parties can make it for the meeting will work fine.

This meeting might come as a surprise when you remember what happened immediately after O.J. died -- LaVergne said he'd make sure the Goldmans didn't get anything ... but a few days later he walked that back, telling us he'd follow the letter of Nevada probate law.

Simpson was ordered to pay $33.5 million to the Goldmans and Browns back in the late '90s after he was found liable for their deaths in a civil trial ... but, interest over time has reportedly inflated the number up into the nine figures.

As for how much the Simpson estate has to fork over ... LaVergne was somewhat vague when we spoke to him on "TMZ Live," but he did claim O.J. did not have millions.