LedBorg Running on DiddyBorg Coding Problem

The problem is that when you reach the while borglights loop it does not get to the end of the handle function.
Each button press makes a call to this function, so the next press is still waiting for the previous one to finish first.

The proper way around this problem is to use threads.
By creating a new thread we can have the LedBorg code running separately to the web handling code.

First we are going to need the borglights to the globals list:

# Global values
global PBR
global lastFrame
global lockFrame
global camera
global processor
global running
global watchdog
global movementMode
global heading
global borglights

It seems like you already have in the handle function, keep that as well.

Second we need to create a new thread class for the LedBorg loop:

# LedBorg colour thread
class LedBorgLoop(threading.Thread):
    def __init__(self):
        super(LedBorgLoop, self).__init__()
        self.start()

    def run(self):
        # This method runs in a separate thread
        global borglights
        global running
        while running:
            # CODE FOR THE LOOP WILL GO HERE

Next we can move your LedBorg loop code into the thread (I have removed the print lines:

# LedBorg colour thread
class LedBorgLoop(threading.Thread):
    def __init__(self):
        super(LedBorgLoop, self).__init__()
        self.start()

    def run(self):
        # This method runs in a separate thread
        global borglights
        global running
        while running:
            while borglights:
                if not borglights:
                   break
                # Loop over a set of different hues:
                for hue in range(30):
                    if not borglights:
                       break
                    # Get hue into the 0 to 3 range
                    hue /= 100.0
                    # Decide which two channels we are between
                    if hue < 1.0:
                       # Red to Green
                       red = 1.0 - hue
                       green = hue
                       blue = 0.0
                    elif hue < 2.0:
                       # Green to Blue
                       red = 0.0
                       green = 2.0 - hue
                       blue = hue - 1.0
                    else:
                       # Blue to Red
                       red = hue - 2.0
                       green = 0.
                       blue = 3.0 - hue
                    # Set the chosen colour  
                    SetLedBorg(red, green, blue)
                    # Wait a short while
                    if not borglights:
                       break
                    time.sleep(0.1)
            time.sleep(0.2)

I have then made some slight adjustments to allow the running or borglights flag to cause an early exit.
Also the final sleep has been moved up so it is outside the while borglights loop to stop the thread being to "busy" when it has no work to do.

# LedBorg colour thread
class LedBorgLoop(threading.Thread):
    def __init__(self):
        super(LedBorgLoop, self).__init__()
        self.start()

    def run(self):
        # This method runs in a separate thread
        global borglights
        global running
        while running:
            while borglights:
                # Loop over a set of different hues:
                for hue in range(30):
                    # Check if we need to end early
                    if (not borglights) or (not running):
                       break
                    # Get hue into the 0 to 3 range
                    hue /= 100.0
                    # Decide which two channels we are between
                    if hue < 1.0:
                       # Red to Green
                       red = 1.0 - hue
                       green = hue
                       blue = 0.0
                    elif hue < 2.0:
                       # Green to Blue
                       red = 0.0
                       green = 2.0 - hue
                       blue = hue - 1.0
                    else:
                       # Blue to Red
                       red = hue - 2.0
                       green = 0.
                       blue = 3.0 - hue
                    # Set the chosen colour  
                    SetLedBorg(red, green, blue)
                    time.sleep(0.1)
            time.sleep(0.2)

We now have a thread which should work, we just need to load it correctly.
I would put this where the other threads are started, before the httpServer = ... line:

# Setup the LedBorg colour thread
ledBorgThread = LedBorgLoop()

The thread should end on its own when the running flag is set to False at the end of the script.