The Celtic defender says he is good friends with his rival for a first-team spot.
Lustig made a successful return to first-team action for Celtic this week, scoring two second-half goals during a 4-0 win over Motherwell - a result that returned the Bhoys to the summit of the Scottish Premiership.
But the Swede says he is good friends with 23-year-old Matthews, whom he is happy for when he starts - even if it means Lustig dropping to the bench.
"Like I said before, there is a really hard competition for places which is good," Lustig told reporters.
“We have been playing together for three years and we have always have a good relationship. We always talk together, so there are no hard feelings there.
“If you have to be on the bench, in one way it’s nice to feel that the guy playing is a good player and Adam and I both feel that way.”
One of Celtic's biggest advantages in Scotland this season is their strength in depth in terms of numbers. As well as the competition for places in defence, Ronny Deila has plenty of options all the way through his side.
Tomorrow, however, may present a tough test of Celtic's squad capabilities at Ross County. The last time the Bhoys traveled to County, they won 5-0. But, the last time they faced the side at home, Deila's men were unable to penetrate their defence in a bore 0-0 draw.
Celtic have hit form, though, and Lustig and co will be hopeful of another convincing win - whoever makes the starting XI.