If you can do it externally, I presume you have some C-code that will do the fit for you. Create a library (on windows a .dll file) with your code and link labview against it. Since it is a normal library, you can debug it rather easily, using standard tools. See the "Using External Code in LabVIEW" pdf-file that comes with LabVIEW 6.
A different method is to use the "Levenberg Marquardt.vi" from the from the Curve Fitting palette. (FDS and Higher only?). This will allow you to specify your own function to fit to (even at run-time). Disadvantage: it is painfully slow, as the maths is interpreted and not compiled as the rest of LabVIEW: a recipe for slowness. But it will allow you to test you fitting.
However, if you make a copy of the "Levenberg Marquardt.vi" (save a
copy as...), it can be hacked to accept vi references and use those for calculations: usually a 10-fold or more increase in speed. Requires some work, and I don't think you are allowed to distribute the result.