In this case I made the lidded cylinder without using a face plate.
First I turned the cylinder
leaving about 1/8 of an inch on each end knowing that those pieces would be cut off, and about 3/4 from one end I cut deeply with my parting tool.
Once the cylinder was round I cut the top quarter off using my table saw sled, so that the cut would be at 90 degrees. I then cut the extra wood off the base, on the table saw again so the base would be flat and square. Next I used a Forstner bit to drill into the bottom section, since I couldn't hollow it out on the lathe. I used dividers to make sure that I was drilling in the centre of the cylinder, if the hole were off centre the top would not fit properly.
The base once drilled is ready for final sanding. I had sanded the cylinder to 400 grit on the lathe.
The top section was now re-installed on the lathe and a tendon cut to fit the bored hole in the cylinder. The other end has the extra wood that will be cut off with a saw once the piece is removed from the lathe.
The cylinder has a flat top where it has been cut off the extra wood and that needs to be sanded carefully to get a nice end grain finish.
The only real downside to making a cylinder like this is the final sanding isn't done on the lathe but by hand. The up side is the money saved.
Once sanded I sprayed the two pieces with 3 coats of varnish.