I have an E3, but I have been offered another position in my field to do some freelance work. Can I work a second job? If so, is getting a certified LCA enough? Or must I go to a US Consulate once I have a second LCA certified?

The E-3 visa is a employer specific visa. The employer must file for an approval for you to work with that employer. Part-time work visas are certainly approvable. Remember, the E-3 is for a professional, so the position must meet that definition. Good luck.