Dear Georgea Sharkey,
Thank you for posting your question on History Hub!
To better assist you, we would need some more information for the individual you're researching. In the meantime, If you haven't done so, please check out this helpful resource for researching and accessing immigration records at the National Archives: https://www.archives.gov/research/immigration/overview
We hope this information was helpful in your research!
The LaSalle Co, IL naturalization records index is available at Illinois, County Naturalization Records, 1800-1998 — FamilySearch.org. One can only view the records at a local Family History Center, once they reopen.
County level Naturalization records are held with the Illinois State archive. Records from LaSalle County can be requested from their office at Northern Illinois University.