USCIS does not list L-2 as a visa that can be applied for with premium processing, but my petition has been submitted with premium processing.
Can I request premium processing for an L-2 when I apply for premium processing on my L-1?
Premium processing is for the petition, not the visa.
Assuming your L-1 petition is accepted you next fill in your DS-160, you also fill DS-160 forms for each family member. You then schedule a consular interview for all family members, giving the DS-160 for references for all the family.