Hi
We often travel out to Lindos in May and October and yes, generally the weather is about the same though the sea is warmer as it's had the sun on it all summer.
Everything will still be open and though it does start winding down i don't think you'll find it much (if any) quieter than May. The only thing you sometimes find in October is that some shops and restaurants won't have full stock in as they're running it down for the winter but it's not a major problem.
ENJOY

We went for 2 weeks on the 12th October last year and weather was fine apart from one day the wind was quite chilly and a bit cold for sunbathing. All shops/restaurants were still open

Thats good then, I am not bothered if we cannot have everything we fancy on the menue, as long as the beer and cocktails are flowing

I go to Lindos the first two weeks in May and first two weeks in October almost every year. I've yet to experience any bad weather...and it's only down the road from Pefkos. Temperatures range from the high 70s to, sometimes, the 90s...it depends on your luck. It can get a little cooler and windy at night but again, cold is relative to what you're used to.
I don't take any heavy clothing...there's plenty of "inside places" to visit. lol
Enjoy yourself.