"Would You Care," 1905, in Levy Sheet Music, by Charles K. Harris (words and music).
1st line- lift your eyes to mine darling
Chorus-
Would you care if I should leave you?
Would you care if we should part?
If someone told you that another won my heart?
Would you care if you found me closely held in some-one's arms?
Would your heart ache just a little,
Tell me darling, would you care?

Is this like the L & S recording?

The Lulu Belle and Scotty recording is available at Homestead Records, but I don't have it and can't compare. Not on The Record Lady.