@Senior_Vagabond That's not really possible - if both lines were 'hot' then the switch would be moot, yes? 

Are you possibly detecting with a non-contact voltage detector? 

It's common for those to falsely detect voltage if the wires are in close proximity to each other (even through the insulation!) 

So I would suggest - turn off breaker, remove the 'dumb' switch, separate the two wires and then turn breaker back on and check again. 

If it really IS live, the other way that can happen is you have a Neutral issue and your system somewhere is using a shared Neutral 

You mention two lights (extremely doubtful that they are wired in series) - do these have separate switches or does that one switch control both? 

If single switch, even if only one load wire leaving the switch box, the second light would be wired in parallel to the first (with the connection to the 'second' taking place at the 'first' light fixture box) 

@Senior_Vagabond 

Think about this for a minute:

If the Load wire was really hot, then the lamp would be on 

Also, the Switch would not be doing anything, since both sides would reputedly be at same potential. 

I think there must be an issue with the Neutral side (of the lamp) and you are reading no-current voltage through the bulb; I suspect if you were to remove the bulb from the fitting controlled by that switch, you will no longer see voltage on that load wire which would validate that route is from where your voltage is coming . That would still require some investigation as to why you are getting voltage via the Neutral so good to discuss with your Electrician. Please do report back on what you find, it's certainly got my curiousity.