Here are some planned protests for tomorrow. Nothing really near the Memorial.
https://www.washingtonian.com/2020/10/08/washington-protests-october8/The closest metro stop is about 3/4s of a mile, Foggy Bottom Metro Station. That's the orange and blue lines.
Come out of the station and turn right and keep walking down 23rd Street until you get to Constitution. Make a left on Constitution and go about 2 blocks and cross the street at Henry Bacon Drive and you're pretty much right there.
It's an easy walk. I used to do it when I worked at State Department on E Street. I'd occasionally go down into the park and walk around the park when I didn't feel like working. The Lincoln Memorial is right there, and at the other end of the reflecting pool is the World War II memorial. If you have time, I suggest going to it, as well.
Remember that you'll need metro fare cards. You can purchase those at Giant grocery stores and, hopefully, at whatever metro you enter at (IF the machines are working, which is always a crap shoot).
If you're driving, you're on your own. :)