To be sure, there are two Tommy Dorseys living and working around the same time. One left his mark on the church, and the other left is mark on the music industry as a Big Band conductor. The latter could be seen filling in for Doc Severinsen as leader of the Tonight Show band. The former made it big in his own way, both in the secular realm early in his life and in the sacred realm later in his life.
As a parish musician, I can relate to Thomas A Dorsey's reflection, "I've been thrown out of some of the finest churches around!" For Dorsey, it was his progressive music that got him in trouble. For me, it was mostly budget cuts. At least that's what they all told me...
Where the black church had been using the spirituals up through this time, Dorsey introduced a new style of music. The spirituals had their roots in the rural south, while Dorsey's songs had their roots in the urban north.
Dorsey was music director at Pilgrim Baptist Church in Chicago from 1932 to 1983, so apparently at least one church decided to keep him around!
I don't know if Thomas A. Dorsey ever went on the Tonight Show like his contemporary Tommy Dorsey did, but you might have found his song, "Precious Lord, Take My Hand," sung by long-time collaborator Mahalia Jackson. This recording artist helped Dorsey's music burst onto the scene. She appeared on many variety shows including The Tonight Show with Johnny Carson.
And if you aren't familiar with Mahalia's rendition, you might be familiar with the one by Elvis Presley.
Getting back to Mahalia, she has a definite style for solo voice. This doesn't always translate into congregational song (anymore than an aria from Handel's Messiah would). Trust me on this, though, Mahalia's style has been used successfully in corporate worship! You need the right congregation, though. Here is a better pace for congregational singing.
Like "Lead Me, Guide Me," Precious Lord is an good choice to supplement your hymnody in the early Lenten season.
who is unable to sympathize
with our weaknesses,
but one who in every respect
has been tempted as we are,
yet without sin.
Let us then with confidence draw near
to the throne of grace,
that we may receive mercy
and find grace to help
in our time of need.
Hebrews 4:15, 16
You can find the complete text for Precious Lord, Take My Hand in Lutheran Service Book, #739.