Write to serial only if the state of a light sensor changes
You wrote: “I am using the Arduino Uno to print to the serial monitor
its state every second.” This is exactly the right thing to do. Make a
record of the analog readings for a few days, then plot the readings as
a function of time.

Once you have a nice plot, take a close look at it. You should be able,
by reading the plot, to decide on a threshold value that you can use to
tell whether the LEDs are on or off. Or, better yet, two thresholds in
order to have some hysteresis.

Then you can write something like this:

const uint8_t LDR_PIN = ...;
const uint16_t THRESHOLD_LOW = ...;
const uint16_t THRESHOLD_HIGH = ...;

uint8_t state = LOW;

void loop()
{
    uint16_t reading = analogRead(LDR_PIN);
    if (state == LOW &amp;&amp; reading &gt;= THRESHOLD_HIGH) {
        Serial.println("Reading is now HIGH.");
        state = HIGH;
    } else if (state == HIGH &amp;&amp; reading &lt; THRESHOLD_LOW) {
        Serial.println("Reading is now LOW.");
        state = LOW;
    }
}