I have created a macro that will add lines to a table with the appropriate
form fields in each cell. However, I don't want people changing any other
part of the document except for being able to edit the form fields and add
additional lines to the table.

Can I run a macro on a protected document?

If not, the only other option is to add a table with a style and then allow
editing of that style. Will that work also?

Thank you!