The two Main dimensions on any pulley are: diameter and center bore.
Beyond that offset belt width & material type used to make it, groove angle.
The outside diameter and center bore are Easy to measure, there are Not a lot of different groove angles used on mowers, especially on idler pulleys.
The offset can be achieved using universal replacement pulleys and spacers, (washers)...
The material used is usually going to be: various materials plastic, stamped steel, cast iron or aluminum... on a mower usually Not critical.
check google:
https://www.google.com/#q=v+groove+idler+pulleys
You will find a LOT of suppliers, this is Not as mysterious as some would lead you to believe. it will be easy to locate a very Good and Low priced Idler Pulley.
:smile:KennyV