I have solved this issue.
What was causing the issue was that in the Firefox settings, I had selected the "Always use private browsing mode" option. After un checking that option the Windy "Lat Lon" setting is preserved when Firefox is closed and restarted.
Private browsing in Firefox deletes history, cookies and other site data when the session closes. Unlike some other options, the Always use private browsing mode doesn't allow the definition of exception to that rule.