What is the best way to ask for a lecturer position in a cold email? I am interested in becoming a lecturer at the school I received my Bachelors. I am in love not only with the school, but the field of communications. The department has been looking for ways to bring in more students, and I feel as if I could become a lecturer there and also rebrand the department. I have spoken with a professor in the department and she gave me the appropriate contact information, but what is the best way to inquire and cold email about it?
If your background is only a BA, it is unlikely that you will be able to snag a position as a lecturer. 

Usually these are highly competitive, and are either:
1. reserved for graduate students in order to provide a stipend, 
or 
2. posted publicly as jobs for PhD holders who have gone the teaching route versus research route.

TBH it sounds like you're interested in working with recruiting for the department, and not actually teaching courses. Lecturer positions pay very little, are highly teaching intensive, and will not offer a lot of time for "rebranding" as you put it. 

It is great that you have enthusiasm for the field, your school, and the department, but it is likely that your passions would be better fulfilled by working with the department in an administrative capacity. I would write a general letter of interest to the department and see if they can propose a position that would fit your background.

Edit: I should say that my response is based on knowing very little about your background. If you do have an MA in the field you can send a CV including teaching experience, cover letter, teaching philosophy, as well as a sample curriculum to the person.