Charles:
The Lee Speed action was never used in a military rifle, although the MLM (magazine Lee Metford) and MLE Mk.I rifle actions are practically the same. If you're not worried about what is stamped on the metal, just get one of those actions and fit up a new barrel with express sights, and fit a sporter stock. Many Lee Speeds had a stock which resembled the cut-down military woodwork anyway.

There was a good 2-page article on the Lee Speed rifle "Rifles at Random" in the International Arms & Militaria Collector magazine (No.22) a couple of years ago, which will give you an idea which grades of rifle had which features. Flick back through the Lee Speed threads on this forum for similar info.

I doubt you will find an article on how to 'make' a Lee Speed as such. What you will be doing is making a Lee Enfield sporter, and how nice you make it is up to you. There are plenty of guidelines on sporterising military actions, such as the NRA Gunsmithing Guide. Even Frank de Haas's 'Bolt Action Rifles' has sections on sporterising each military action, he shows a custom Lee Enfield with a one-piece stock IIRC.

You have a specific project in mind, I assume? Be sure to share it with us as you progress!