I've put the entry *@domain.com in a lookup database, but it isn't working. The expansion I'm using is:

${lookup{${lc:$sender_address}}dbm{/the/file} ...

As no sender address will ever be *@domain.com this will indeed have no effect as it stands. You need to tell Exim that you want it to look for defaults after the normal lookup has failed. In this case, change the search type from dbm to dbm*@. See the section on*Default values in single-key lookups* in the chapter entitled File and database lookups in the Exim manual.