James needs four 3-pointers to pass Steve Nash for 19th on the NBA's all-time list.
Ingram has missed seven straight games with a sprained ankle. Rondo has missed the 17 games since he underwent surgery to repair the third metacarpal in his right shooting hand.
But the Lakers, who have won five straight at home, will be short-handed at center.
"We got a sick team right now," coach Luke Walton said. "... [James] didn't come to shootaround, so he is getting rest right now. Knowing LeBron, he is doing everything humanly possible to get himself ready to be able to perform tonight."
Walton said that starting center JaVale McGee will sit out his third straight game with a respiratory infection and other flu-like symptoms. Centers Tyson Chandler and Ivica Zubac also had IVs for precautionary reasons as they try to stay healthy.
Information from ESPN's Ohm Youngmisuk was used in this report.