What are the benefits of hiring a lawyer after I have submitted my asylum application?

unfortunately you realized that a bit late, but still an attorney can help you with the follow up on your application and prepare you for your interview.

A lawyer can't speed up the process, but a lawyer experienced in asylum cases can definitely help prepare you for the interview. Additional evidence can be brought to the interview, so there is still time to obtain witness statements, get documents that will corroborate facts that are important to your case, gather information regarding human rights conditions in your country, and work with you on other matters that will be very important to the success of your asylum claim.

Same as hiring a lawyer before you submitted the application. Submitting the application is just the beginning of a very tumultuous journey. If your understanding of legal help is speeding up the process - you need no lawyer. If you want to win, know that - statistically, majority of asylum applications handled without an attorney are denied.