I'm not satisfied with your diagram. I don't want to know how the relay board works . I want to know how you have it connected. You don't have a schematic because your voltages are missing.
Get a piece of blank printer paper and draw the schematic. Forget about the photos of the relay board. We are very familiar with those. Just draw the relay board as a box and label the pins. Show what pins connect to what and where and the voltages. Post a photo of the schematic. Post your code.
This circuit is dead simple. There is no reason why you should have any problem.
Disconnect the lights from the relay board and power them on and off with a switch. If that works, the lights are fine.
Next, connect an ohmmeter to the N.O. and common terminals of the relay and turn it on and off and see if the there is continuity when you turn it on. If so , the relay is fine.
If so, connect one end of the lights to the AC LINE and the other end to the N.O. terminal.
Connect the common terminal to the AC NEUTRAL.
Test the relay again. The lights should turn on.
I also have the input to the relay working correctly. I can switch on and off the relay but the lights never respond accordingly. I'm also tried swapping the two wires in the two NO/Common gates. Is there something I'm missing?
Yes, there is. If you tried this you are missing a lot. It's ac and it's a relay. What possible difference could it make if you swap those two connections ? If you tried something like that, your understanding of electronics is so minimal that anything at all could be wrong here. We have to consider you are doing things that are so far out of the realm of expected possibility that we can't even imagine them.
Post another photo of your circuit but from directly above instead of from the side. Make it a close up close enough that we can see where all the wires go.
Is the relay input active HIGH or active LOW. (does the relay turn on with a HIGH or a LOW ?)
. I also have the input to the relay working correctly. I can switch on and off the relay but the lights never respond accordingly
The relay is either working or it is not working. It is a simple matter to connect a meter to the contacts to measure continuity or make a continuity tester with an led and a resistor so the relay turns the led. On
Are the relay CONTACTS closing or not ? That means you need to test the contacts. We don't really care about the leds on the relay board. We are interested in the contacts.
On a lesser important note: the relay terminals are called "TERMINALS" (NOT PORTS)
A "PORT" is something else entirely , which, based on your post, I don't think you are quite ready for.
The relay contacts are not "ports" because they are SPDT contacts. A "port" is an electrical connection like a "+" and a "-" of an arduino GPIO , with the GPIO being the "+" and the GND being the "-" , with current flowing through them, as opposed to "across them" as in the case of contacts which connect to each other.
FYI, in electronics , when discussing AC , there is no such thing as "Fire" and "zero". The HOT is called "Line" and the other wire is called "Neutral"
Is that something that came from the relay vendor