Use a switch to override Arduino program
Add a boolean that indicates whether the leds are on because of the time. replace digitalWrite with setting that boolean.

Then you add an if:

bool switchOn = digitalRead(switch) == HIGH; //when using pulldown configuration
bool timedOn =false;

if (today == "Thursday") {
    if ( 15 &gt; t.hour &amp;&amp; t.hour &lt; 22) {
      timedOn = true;
    } else {
      timedOn = false;
    }
} else if (today == "Friday") {        
    if ( 16 &gt; t.hour &amp;&amp; t.hour &lt; 23) {
      timedOn = true;
    } else {
      timedOn = false;
    }
} else {
    timedOn = false;
}

if(switchOn || timedOn){
    digitalWrite (Relay, HIGH);
} else {
    digitalWrite (Relay, LOW);
}

if(switchOn){
    digitalWrite (indicator, HIGH);
} else {
    digitalWrite (indicator, LOW);
}