Weird arduino bug, using microphone and relay
I've looked through your code and can't see anything obvious that is causing the problem, so I have refactored it a bit in the hope that the problem becomes more obvious.

/* DEFINE PINS */
const int PinBuzzer = 2;
const int PinMic = 0;
const int PinRelayLED = 9;
const int PinRelayLights = 8;

const int sampleWindow = 50;
const int MaxSamples = 50;

// Simple enumeration to clarify which state is on and off.
enum EOnOff { Off, On };
EOnOff lights = Off; //lights on or off
EOnOff leds = Off; //leds on or off

double soundArray[MaxSamples]; //array to check claps


void setup() 
{
    pinMode(PinRelayLED, OUTPUT);
    pinMode(PinRelayLights, OUTPUT);
    digitalWrite(PinRelayLED, ConvertOnOff(leds));
    digitalWrite(PinRelayLights, ConvertOnOff(lights));
}


void loop() 
{
    for (int sample = 0; sample &lt; MaxSamples; ++sample)
    {   // Get the samples
        soundArray[sample] = getVolts();
    }
    switch (clapCount())
    {   // Analyse the samples
    case 2:
        lights = ChangeRelay(lights, PinRelayLights);
        playSound();
        break;
    case 3:
        leds = ChangeRelay(leds, PinRelayLEDs);
        playSound();
        break;
    }
}

/// Count the number of 'claps' in the sample data
int clapCount(/*clap array is global*/) 
{
    int claps = 0;
    for (int sample = 0; sample &lt; MaxSample; ++sample) 
    {
        if (soundArray[sample] &gt; 3.0 &amp;&amp; soundArray[sample] &lt; 3.5) /* Why 3.5?? */
        {
            ++claps;
        }
    }
    return claps;
}

/// Convert an EOnOff value to a HIGH or LOW value.
// OFF = HIGH
int ConvertOnOff(const EOnOff&amp; state)
{
    return state == Off ? HIGH : LOW;
}

/// Change a relay to the given state.
/// Return the new state.
EOnOff ControlRelay(const EOnOff&amp; state, const int&amp; relayPin)
{
    EOnOff result = state == On ? Off : On;
    digitalWrite(relayPin, ConvertOnOff (result));
    return result;
}


/* gets mic volts */
double getVolts() 
{
    const unsigned long startMillis = millis();  // Start of sample window
    unsigned int signalMax = 0;
    unsigned int signalMin = 1024;

    unsigned int sample;
    // collect data for 50 mS
    while (millis() - startMillis &lt; sampleWindow)
    {
        sample = analogRead(PinMic);
        if (sample &lt; 1024)                  // ?? Should this be 1024 or signalMin?
        {
            if (sample &gt; signalMax) 
            {
                signalMax = sample;  // save just the max levels
            }
            else if (sample &lt; signalMin) 
            {
                signalMin = sample;  // save just the min levels
            }
        }
    }
    const unsigned int peakToPeak = signalMax - signalMin;  // max - min = peak-peak amplitude
    const double volts = (peakToPeak * 5.0) / 1024.0;       // convert to volts
    return volts;
}

void playSound() 
{
    tone(buzzer, 1000);
    delay(100);
    tone(buzzer, 500);
    delay(100);
    noTone(buzzer);
}


What I have tried to do is to reduce the number of lines of code.  If there are less lines then there should be less bugs :)

You used a bool to record the on off state, I changed that to an enumeration because that adds a bit of clarity, and when working with mains voltages I like things being clear.

I changed your while loop into a for loop, I think it looks cleaner.  This was also the reason I changed your if statements into a switch statement.

The guts of the if statements have been removed and placed in a function ChangeRelay(), it returns the new state of leds or lights.  I could have gone with a reference to make state an in out parameter, but decided a return was simpler.

ClapCount() and GetVolts() are relatively unchanged apart from a bit of const'ing of variables to make things easier to read.  Also you might have noticed I, j and N have all been removed, because single letter variable names are my nemesis, who knows what q means and why r and t are being added to it to make z?

ControlRelay lets you route all you relay switching through one function, if there was a copy and paste bug in your code (which I don't think there was) then they will either all work or not work now.

There is a big difference between "my" code and yours, you won't be able to switch both on at the same time because the switch statement won't let you.  So in a way you problem is solved.  If you really wanted to you could add:

case 5: 
    lights = ChangeRelay(lights, PinRelayLights);
    leds = ChangeRelay(leds, PinRelayLEDs);
    playSound();
    break;