The Ahmaud Arbery murder case is moving at lightning speed ... seemingly light-years faster than the Breonna Taylor case ... and TMZ's learned both of their mothers will join forces in their fight for justice.

Lee Merritt -- attorney for Ahmaud's mother, Wanda Cooper-Jones -- tells us ... Ahmaud's mom is all set for a face-to-face with Breonna's mother, Tamika Palmer, Thursday in Louisville. It will be their first face-to-face meeting.

Wanda, who flew from Georgia to Louisville Wednesday night, is in for a busy day ... we're told after her sit-down with Tamika, she's scheduled to meet with lawmakers and local activists to fight for justice for Breonna.

Merritt will accompany Wanda as they lobby to have the Louisville police officers involved in Breonna's death arrested and charged. They will also lobby for federal intervention ... the feds could charge a civil rights violation ... something they did in the Rodney King case to secure convictions.

One item at the top of the agenda -- the Justice Act, which was just introduced in the State Senate and calls for police reform, transparency and accountability. Merritt tells us the bill doesn't go far enough to help Breonna's family get justice.

As we reported ... the 3 individuals charged in Ahmaud's murder -- Travis McMichael, Gregory McMichael and William "Roddie" Bryan -- were indicted by a grand jury Wednesday, and are each facing 1 count of malice murder, 4 counts felony murder, 2 counts aggravated assault, 1 count false imprisonment and 1 count criminal attempt to commit false imprisonment.

Meanwhile, the cops involved in Breonna's death have yet to be arrested. As you know, Breonna was shot 8 times after cops entered her home in the middle of the night looking for someone else. They also lied and said in the police report she was not injured.