Since a layout can display data for any number of different customers, you wouldn't want to lock a layout. But you can lock a record in that table by capturing a signature in a container field (Using FM Go here perhaps?).
If you have used Manage | Security to set up accounts and passwords for your users, you can set up custom access privileges for Records and use the Limited option to open a calculation dialog where access to a record is permitted only if the calculation evaluates as True. YOu might use:
IsEmpty ( signatureField )
as such a calculation.
See "Editing record access privileges" in FileMaker Help and check out this particular sub section: "Entering a formula for limiting access on a record-by-record basis" for a detailed description of how to set this up.