Make sure that the Work Email field in LinkedIn is mapped to the standard Email Address field. Also make sure the field is required on your LinkedIn forms.
Would I need to verify this globally or is this something that can be designated within a specific program/active trigger?
Linkedin field mappings are global, setup within the launchpoint integration. They are the 4th and last thing you setup (and it can take some time for the window where you edit the mappings to contain data when you are setting up the integration) if your clicking fast - you may click past it, and if you add new fields you need to set this up for each new field.
We also have a "work email address" field on our Linkedin form & this is what my setup looks like.