You sure can. Tell them your plans. Both my letters were from classes a couple years prior to my application, but they were more than happy to write them and update them.
I applied in 2014. I asked professor from Spring 2012 for a letter. Explained my background: nontrad, getting letters will be tough since I didn't take sciences in undergrad. I had an extended timeline because I was working fulltime and doing 48 hours. He wrote it, submitted it to a premed committee. I chose not to use the committee, kept in contact with him once or twice a semester, and he updated it and sent it to Interfolio. All my updates were short and sweet: hope all is well, would you still be willing to update the letter? If so, my grades are XYZ.
I used my pathophysiology professor, who I took a class with in the fall of 2010. I knew that person professionally, academically, and personally though so the letter I got from that professor really covered 5 years of a ton of stuff.
Try hard to have them write an initial one, and then have them update it. I got As in both their classes, and with the exception of O-Chem I got As in all my other science classes. So I didn't give them reason to need to change the letter...
