Lincoln did have 2 sons that died young before he was assassinated. Tad wasn't one of them. Trump was probably referring to Willie but got the name wrong:

Edward Baker Lincoln (March 10, 1846-February 1, 1850) was the second son of Abraham Lincoln and Mary Todd Lincoln. Eddie died aged 3 years 11 months. Census records list "chronic consumption" (tuberculosis) as the cause.

William Wallace Lincoln (December 21, 1850 -February 20, 1862) was the third son of President Abraham and Mary Todd Lincoln. Willie was named after Mary's brother-in-law, Dr. William Smith Wallace. He died of typhoid fever at the White House, during his father's presidency, age 11.

Thomas "Tad" Lincoln (April 4, 1853-July 15, 1871) was the fourth and youngest son of the 16th President of the United States Abraham Lincoln and his wife Mary Todd Lincoln. On Saturday morning, July 15, 1871, Lincoln died at the age of 18 at the Clifton House hotel in Chicago. The cause of death has been variously referred to as tuberculosis, a pleuristic attack, pneumonia, or congestive heart failure. In an obituary, John Hay affectionately referred to him as "Little Tad.

"Robert Todd Lincoln (August 1, 1843 " July 26, 1926) was an American lawyer and businessman."

I've been to his home, Hildene, in Vermont. It's a big beautiful place: