If the lattice is that thin, it would actually be cheaper to just replace it.
Seriously.
Lattice runs about $35-$40 for a 4x8 sheet.
Stripping it would cost several times that. Plus, you face the potential that it will just come apart anyway.
More aggravation and the customers perception isn't as good if they think you should have thought of that in
the first place.
Once you replace it, staining it will look better and last longer and the customer will consider you more in touch with
your work.
Back to you~
Rod