Replicating Lidar lite what emitter to use?
First, there is no worry about recreating a commercially available product if it is for your own use, and not part of a business enterprise. Furthermore, if Lidar Lite is no longer available the company clearly is not going to come after you, and there is no reason in the world not to use their ideas for your own enjoyment.

There is no simple answer to your question. A laser is the obvious choice for the emitter, and a silicon photodiode for the receiver. However, the laser is favored primarily because it's relatively easy to produce a small beam. If you're willing to spend more effort on optics, an LED is certainly possible.

Since you're obviously not very experienced, I'd recommend one of two approaches. At 40 meters, round trip for light is about 260 nsec. Call it 300 to give yourself some leeway. If you want to operate at longer ranges, assume a longer delay, but for now let's go with 300 nsec. A square wave at 3.3 MHz will have a 300 nsec period, so use half that frequency, or 1.65 MHz. What you want to do is exclusive OR the transmit and receive signals, and analyze the result. Alternatively, you can do what the commercial rangefinders do. Invert the receive signal and use it to drive the transmitter. The result (assuming you have adequate signal-to-noise) will be a square wave with period proportional to distance. Either approach will work, although you haven't specified your minimum range, and the second approach will not work well at close range due to the high frequencies involved.

I suggest you read this Lidar Lite paper  and pay attention to things like the bandpass filter they use. If you're going to be using your unit in sunlight, be aware that you need a very narrow filter to avoid your detector getting saturated.

If you avoid the correlation technique Lidar light used you'll work at much lower frequencies although you'll need to be careful to get fine resolution. You haven't specified your requirements, but presumably at 40 meters you're not interested in very fine measurements. You clearly have a great deal of learning and experience waiting for you. Good luck.