Love, 28, underwent a scan on the knee on Sunday after experiencing pain in the joint during Saturday's 125-109 win over Denver.
The four-time NBA All-Star had already been ruled out of Tuesday's road game against the Minnesota Timberwolves.
But Lue said Love now faced a further examination on Tuesday to assess his injury.
"Always concerned when guys are going down," Lue said. "And we're already limited as it is. Definitely concerned, but gotta see how he feels. Just, get evaluated (Tuesday) and see how he feels."
Love is averaging 20.0 points, 11.1 rebounds and 1.9 assists for the Cavaliers, who have won five of their past six games and improved to 37-16, the best record in the Eastern Conference and fourth-best in the league overall.
Channing Frye is likely to replace Love in the starting lineup for the Cavaliers, who could opt to bench Love through the break for next Sunday's NBA All-Star Game.
Cleveland will visit Minnesota on Valentine's Day and play host to Indiana on Wednesday but after that will not play again until February 23 when New York visits.
Love was named a reserve for the Eastern Conference in the annual All-Star matchup to be played at New Orleans.