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My answer might not be what you'd expect but I'll try anyway.

Did you troobleshoot your serial communications ? Try doing a simple programm for both cards and try sending data from one to another.

uno code (not tested)

mega code (not tested)

Did you check your connections ? Tx (mega) to rx (uno) and rx (mega) to tx(uno)

In your setup() on your arduino mega

void setup()
{
  Serial.begin(9600);
  lcd.begin(16,2);
  pinMode(22,INPUT_PULLUP); // Reed switch - Row1
  pinMode(24,INPUT_PULLUP); // Reed switch - Row2
  pinMode(26,INPUT_PULLUP); // Reed switch - Row3
  pinMode(28,INPUT_PULLUP); // Reed switch - Row4
  pinMode(30,INPUT_PULLUP); // Reed switch - Row5 
  pinMode(32,INPUT_PULLUP); // Reed switch - Row6 
  pinMode(34,INPUT_PULLUP); // Reed switch - Row7 
  pinMode(36,INPUT_PULLUP); // Reed switch - Row8 
  pinMode(2,INPUT_PULLUP);// Push Button
  pinMode(38,OUTPUT);
  pinMode(40,OUTPUT);
  pinMode(42,OUTPUT);
  pinMode(44,OUTPUT);
  pinMode(46,OUTPUT);
  pinMode(48,OUTPUT);
  pinMode(50,OUTPUT);
  pinMode(52,OUTPUT);
  pinMode(3,OUTPUT);
  digitalWrite(38,HIGH);
  digitalWrite(40,HIGH);
  digitalWrite(42,HIGH);
  digitalWrite(44,HIGH);
  digitalWrite(46,HIGH);
  digitalWrite(48,HIGH);
  digitalWrite(50,HIGH);
  digitalWrite(52,HIGH);
  digitalWrite(3,LOW);
}

I don't see the Serial1.begin(9600) but you mentionned it above.

I hope this helps, sorry if I've not solved your problem.