My linings are hand-sewn using saddle stitch, which merits its own section: Saddle Stitch
A lining might be considered as simply an extra touch of luxury, but its real significance is in how the strap feels and behaves in use.
Calfskin is the usual lining material. Being finer-grained than the main layer, it is softer and smoother than an unlined strap.
Lined or Unlined?
This might or might not match your needs.
It should feel more comfortable against your skin, compared with an unlined strap.
It will also move more easily on your shoulder with day-to-day clothing.
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