How can I get SSIS Lookup transformation to ignore alphabetical case?

There isn't a way I believe to make the transformation be case-insensitive, however you could modify the SQL statement for your transformation to ensure that the source data matches the case of your comparison data by using the LOWER() string function.

Set the CacheType property of the lookup transformation to Partial or None.

The lookup comparisons will now be done by SQL Server and not by the SSIS lookup component, and will no longer be case sensitive.