At the time Elmer's book was written hardly any home workshops had a mill and the lathe may well have been a treddle lathe, same with many of the model engineering designs about today they were all done at a time when the lathe was the main workhorse.
So they can all be done on just a lathe, though some lathes may be better suited than others eg the Myford with it's many tee slots and a handwheel on the leadscrew is more suited then a machine with no slots and just the carriage handwheel to put on a cut.
It can be done, that Minnie Traction engine in my avatar was done without a mill but as others have said it is easier on a mill and with the relatively low cost of them now the money spent on a half decent vertical slide etc could be better put towards a small mill.
Your set of barstock for the beam engine will be a bit easier than as set of castings and looking at the drawings the minimal amount of milling could be done without the need for even a vertical slice, just clamping the work to the cross slide or making use of the tool post to hold the various bits of stock. Elmer would also have made more use of the common or garden file than a lot of people seem to want to do these days!
Edited By JasonB on 03/01/2022 07:18:41