Q: Can an older iPad run Spotify without lag?

I have an iPad 2 iOS 8.3 and the Spotify App runs fine.  As long as you have a dependable wifi network you should be fine.  As far as I know, you cannot run Spotify on the original iPad (1st gen)

receiving the stream is a network speed thing, decoding and playing the stream is not very demanding

You should pay more attention to the iOS upgradeability instead of (horse)power. As of today Spotify requires iOS 7 and later. That rules out all devices that can't upgrade to iOS 7 or later versions. I guess horsepower comes into play as well because iOS 7 or later versions demand more power.

Any iPad can run Spotify just fine as long as there is a decent enough internet connection.

While the current version of Spotify does require iOS 7 at least, there is a compatible version of Spotify that works on the first generation iPad just fine.

Just downloaded it from the app Store to try it out on my old first gen.

Install the latest compatible version of an app on an earlier version of iOS or OS X - Apple Support

With that said, if you just want it to run Spotify, I'd go for an iPod touch. cheaper, and smaller foot print.