In order to put together this speech, the first thing you'll need to understand is the meaning of the word "timeless". Something timeless, in a nutshell, is something that does not change with the passage of time. To give an example, love is timeless, as it has been experienced in every age since the dawn of time. A fashion trend, on the other hand, is not timeless, because it will change with every season.
The first element of timelessness in this story is that Meursault's mother passes away. Losing a parent is, unfortunately, a timeless experience that nearly everyone will go through. While it is odd that he handles this with almost no emotion, the experience of loss is still timeless.
The pursuit of love and/or carnal pleasure is also a timeless part of life, and is showcased in this book by Meursault and Marie's relationship.
Criminal activity and psychopathic behavior, unfortunately, are also a timeless element of life. When Meursault commits murder, he shows the same lack of emotion that he showed when his mother died.
The legal process, though manifested in various different ways through the ages, is also a timeless part of life. In this particular case, the legal process results in a guilty verdict and a death sentence. The timeless reality is that if you commit murder, you will be punished.
Remember, every speech should have a powerful interest to draw your listener in. It should be divided into an introduction, a body, and a conclusion.