Trump has 36 percent support, with Rubio at 27 percent.
Lee is the first sitting senator to endorse the Texan.
The poll shows a closer race than other recent surveys.
The GOP front-runner will address supporters at the Crown Center Coliseum in Fayetteville, N.C.
Sen. Bill Nelson (D-Fla.) thinks Trump will beat Rubio by double digits in Florida.
Fiorina ended her own GOP presidential campaign last month.
Cruz rode the endorsement of Rep. Raúl Labrador to victory.
John Kasich had thrown everything at winning the Rust Belt state.
The win gives Trump bragging rights in territory that historically would be Cruz country.
About 7,000 TV ads attacking Trump aired over the last seven days.