The Lakers, who hadn't won more than two in a row until their current run, opened a three-game trip with a 107-101 overtime victory at Dallas on Saturday night.
The win came on the heels of three straight victories at home, including a 93-81 stunner over the San Antonio Spurs.
In the Grizzlies, the Lakers will see a familiar foe. The clubs already have met twice this season, both times in Los Angeles, with Memphis getting a split with a 109-99 win on Dec. 27.
The Lakers won the first head-to-head 107-102 in November.
Tyreke Evans had 32 points for Memphis in its win over the Lakers last month. And the first-year member of the Grizzlies hasn't slowed down much in his team's six games since then, scoring 22 or more points four times.
Interestingly, the Grizzlies and Lakers have continued to share the news in recent weeks without having played. David Fizdale, who was fired as Memphis coach on Nov. 27, has been rumored to be a possible replacement for the Lakers' Luke Walton.
Fizdale hasn't commented on the Lakers, but he did take time recently to say thank you to the Grizzlies for a year-and-a-half shot at being an NBA head coach.
"I don't have any bitterness toward anyone," said Fizdale, who compiled a 50-51 record as the Memphis coach. "I only have fond feelings for everyone. ... I hold no hard feelings toward the Grizzlies. They gave me an opportunity to see if I can do this."
Fizdale was fired after a 7-12 start this season. The club has done worse under interim coach J.B. Bickerstaff, going 6-16.
Interestingly, Walton has led the Lakers to a nearly identical record -- 7-16 -- since the day Fizdale was fired. But that includes the current four-game winning streak that has quieted the talk of a need for a new coach.
In fact, Walton received support on Twitter from both Lakers owner Jeanie Buss and team executive Magic Johnson during and after the Dallas win Saturday.
Johnson's remarks included, "Coach Luke Walton has the Lakers playing some of their best basketball of the season."
While noting he doesn't have a Twitter account, Walton declared after the game that he appreciates the support.
"Jeanie's always been great," Walton insisted. "So there's no doubt that they support me."
Improved play of late from Julius Randle has helped the Lakers turn things around. He had a 23-point, 15-rebound outing against Dallas, his fifth double-double in the last eight games.
The Grizzlies have beaten the Lakers six straight times at home. The last time the Lakers won at Memphis was December 2013.
Kyle Kuzma was the individual star when the Lakers beat the Grizzlies in November. The rookie had 13 points and 12 rebounds.
Kuzma, the 27th overall selection of last June's draft, ranks second among all rookies this season in scoring (16.7 points per game) and fifth in rebounding (6.3).