When later apply for the residency match using ERAS, you will be asked to upload your letters of recommendation via special forms. These forms ask you do notify the writer of the LOR to send the "Original Document" to ERAS support services.
So the best way to go about is that you ask your senior or professor or whoever you'd like to write you an LOR by the time you finish working with him/her. Then again you contact them at the time you apply for ERAS to write anew up to date LOR and send it to ECFMG.
Up to date LORs are very important. Program directors usually disregard old LORs.