UPDATE: Due to the COVID19 pandemic, and until further notice from the US Dept of State, only applications for Passport Renewals (form DS-82), Second Limited Passport, Name Change and Second Passport Renewals can be submitted by third party service providers such as Peninsula Visa. Expected turnaround time for these expedited services through Peninsula Visa currently is 4-6 weeks. We expect services to return to normal by early 2021 pending notification from the US Dept. of State.
If you have lost your US Passport Card, you must apply on forms DS-11 and DS-64 as you would normally do in the case of a lost Passport Book. You may submit your current US Passport Book as proof of your US citizenship, or a certified copy of your birth certificate which would be the better choice. This way you will not be without your passport should any travel plans arise during the processing time for the Passport Card.
The Department of State's online Passport Application System will automatically generate the correct forms based upon how the questions are answered in regard to any lost passport book or passport card.
If your primary passport book is in need of renewal due to pending expiration or running out of pages AND you have been issued a Passport Card that you have since lost or was stolen, you will not be eligible for Form DS-82 which does not require a personal appearance on your part. You must file on forms DS-11 and DS-64 and make a personal appearance at a local US Passport Acceptance Facility, which usually is a designated US Post Office or County Clerk.
Note: At that time, you may or may not apply for a new Passport Card in the same application.
A complete nationwide list of facilities may be found here: https://iafdb.travel.state.gov/