DKY,
I've hit this before. You can make the quotes not appear by using
R1C1-style addressing instead of A1 style. There is information in the
VBA help about R1C1. It's a tricky line to write and get the
parentheses and quotes correct.
Here is an example using EXACT, which I know a little better than
VLOOKUP

j = 3
ActiveCell.FormulaR1C1 = "=EXACT(R[1]C[1],D" & j & ")"

In the example above, the first parameter uses R1C1 and does not come
out quoted, and the second uses A1-style, and does come out quoted.

Note: R[1]C[1] is a relative cell reference, one over and one down from
the activecell. So there's an extra step if you need absolute.

Kevin