LOS ANGELES—Even on a Los Angeles Lakers squad teaming with established veterans, Anthony Davis has had to take on more of a leadership role with LeBron James sidelined. On Monday night, Davis showed his mettle and then some despite dealing with some ailments of his own. The All-Star forward had 32 points and 12 rebounds as the Lakers beat the Charlotte Hornets 126–123 in overtime. “He’s dealing with a lot of stuff and toughing it out,” coach Frank Vogel said. “He made some big buckets and was terrific on the defensive end as well.” Davis has been dealing with a right thumb sprain and an illness. He said he threw up at the end of the third quarter, but that wasn’t going to sideline him. “I had 43 minutes of work. Now, I have 48 hours to replenish,” Davis said. “With LeBron out, we don’t have all our guys. I …