I'm trying to light my LED strip while running another program, unfortunately the example below uses the delay() function which is interrupting my other program.
The demo Several Things at a Time illustrates the use of millis() to manage timing without blocking. It may help with understanding the technique.
Note how each function runs very briefly and returns to loop() so the next one can be called. None of the functions tries to complete a task in one call. And there may be dozens of calls to a function before it is actually time for it to do anything.