Receiving serial data in acsii, how to split it.
This:

if (Serial.read() == le)
{ }


looks very suspicious - sometimes it can read the C or L and therefore render the rest of your code useless.

Also Serial.parseInt shall be avoided - it returns the first thing which looks like a number, and will not wait for all three numbers.

However, your problem is likely the DMX write speed. While the DmxSimple.write is getting executed, no new incoming message can be processed. Depending on your actual Arduino board and chip, there is some buffer, but the solution is not rocket-proof at all.

You can:


make a solid protocol between the PC and the Arduino, i.e. the PC sends one command, arduino sends it out over the DMX, and Arduino answers an OK to the PC. The PC will not send out any new command unless it has received an OK first.
avoid these ad-hoc mess, i.e. serial-reads and serial.printlns here-and there.


For example, if you change the protocol so: CxxxLxxxE (E stands for end) you can utilize readStringUntil to read the input until a separator, and then use the toInt method to actually convert the read data to integer:

void loop() {
    strDummy = Serial.readStringUntil('C');
    strC = Serial.readStringUntil('L'); // xxx from CxxxL
    strL = Serial.readStringUntil('E'); // xxx from LxxxE
    channel = strC.toInt();
    value = strL.toInt();
    DmxSimple.write(channel, value);
} 


After learning that it is not possible to change the protocol, here is a new plan

int channel;
int value;
void loop() {
    if (Serial.read()=='C') { // wait for a C
        channel=Serial.parseInt(); // parse till first non-number
        value=Serial.parseInt(); // parse till first non-number
        DmxSimple.write(channel, value);
    }
} 


See https://www.arduino.cc/en/Tutorial/ReadASCIIString for a tutorial. Note that Arduino Serial commands are pretty confusing sometimes :) for example, parseInt will actually consume one non-number character implicitly after parsing a number.

Also note that this solution works well if the command is sent as one batch. If you are trying to send the command manually, e.g. from a terminal window, character by character, parseInt may time out. Consider increasing the timeout to 10 seconds or more by https://www.arduino.cc/en/Serial/SetTimeout