I must not be understanding what the problem is.
Just now I named a range lfk which I defined in the Name Manager as =Sheet1!$A$1,Sheet1!$B$2,Sheet1!$C$3,Sheet1!$D$4
Then I entered the formula
=SUM(lfk)
which returned the same result as both the formulas I posted, which was what I expected.
What am I missing about what you are expecting?