A lead washer is for moisture sealing so would be pointless if fitting a bush.
The washers are used with flanged couplers as a plain coupler would cut through it.
That's a flanged coupler so will be fine to use with the lead washer, the washer goes on the outside of the box and screwing the brass bush in will compress the lead, forming the seal. It's really designed for outdoor use to keep water out, but if you've bought them you may as well use them.
If you don't already have one, a bush wrench is handy for tightening the brass bushes when they're obscured by the faceplate mounting tabs on the side of the backbox.