The singer was out Sunday with her rumored GF for what we're told was a lunch date in the L.A. area -- with none other than Miley's mom, Tish, tagging along for the ride ... again.

You'll recall ... the trio went out for some grub together just a few weeks ago -- this shortly after Miley and Kaitlynn returned to the States from their Italian vacay ... and obviously very shortly after Miley announced a split from her estranged-hubby, Liam Hemsworth.

TMZ broke the stories ... Liam recently filed for divorce from Miley, but she'll keep the pets they owned together when everything's said and done. It's been pretty nasty thus far.

As for this, Miley and Kaitlynn have been fairly inseparable since they touched down in L.A., when they drove home in the same car. Of course, they've each had solo outings ... but more often than not, they seem to be tied at the hip ... and Kaitlynn's clearly gotten familiar with mom.

Meanwhile, Liam's been laying low in Australia ... hanging with his brother, Chris, and the rest of the fam there. More recently, he seems to be turning his focus on a new movie he stars in called "Killerman." LH plays a guy who lost his memory in a drug deal gone wrong.