Yes, this could be done with a CAML query, but I wanted to keep it simple.
I need to get items created in ascending order (oldest first).
My solution:
SPFileCollection items = web.GetFolder(sLawsonReports).Files;
//sort the files so we get the oldest first
List<SPFile> sortFiles = items.Cast<SPFile>().OrderBy(file => file.TimeCreated).ToList();