"I don't believe 20th century LC Smith barrels were 1020 for a minute. 1020 is stuff you use for making muffler tubing not gun barrels. If you've ever machined 1020 you'd understand that it isn't suitable for machining a gun barrel either. It is so long grained and leaves such a poor finish that you would have to invest in additional finishing processes that cost a lot of time and money."
Chuck, Tom Martin was correct, the steel used for most L.C. Smith parts including the barrels and receiver was 1020 steel.

This cannot be for all, because most had different types of barrel on them and so I would imagine, other steels. The highest was Sir Josheph Whitworth, down to the lowest Royal Steel on the lowest grade hammer gun. I don't know what the barrels on this page are for, but it clealy shows 1020.
At the top right hand side, you can see the word Featherweight, so this has to be after 1907.
An interesting site on the properties of 1020
http://www.suppliersonline.com/Research/Property/metals/819.asp