Is there a way to lock certain parts of a document but leave the rest unlocked?

Only 8 years late here but YES there is. It works great. I used it for a digital copy of my book Servant Leadership Manaul: Education, Assessment, Training, and Organizational Development Activities by Daniel G. J. Kuchinka. See this for simple instructions: https://acrobat.adobe.com/us/en/acrobat/how-to/create-fillable-pdf-forms-creator.html

ok - not ideal.  But we have the same issue.  We want out techs to complete customer and model information and then the client the remainder.  You can lock fields after they have been filled - but then why make them fields just use the word doc as a template for the form.  What we did - was we had the tech fill out the model, SN, etc and then with the client complete the rest of the information.  At the end of the visit she will print the file to PDF which locks down everything and removed all form fields - so what is - is.

What sort of editing will they be doing?

Not possible. Security and encryption on a PDF file cannot be applied on a per-page basis.