my mom lost the ID and she want to go to DMV to make an senior Card, so does she need go on line to make appointment?

Yes she does. Your mom have to go to the DMV near your home, line up to get the number and make follow instructions of DMV staffs.

You can go to DMV early morning and you can finish it , they are doing their best on DMV .

Either way. Appointments are faster. Unless you want to wait in line for 1-2 hours depending on the way.