Maximum separable distance between Micro-controller and LM35 (temperature sensor)
As always, it depends.

The longer your wires are, the more prone they are to pick up noise and hum from nearby electromagnetic sources like motors etc. You can prevent that by using shielded cables. Those made to route audio signals around are pretty good.

This however will increase the cable capacitance. If you look into the data-sheet of the LM35 you'll see that the maximum capacitance it can drive directly is around 50pF. You will easily exceed this limit with a longer shielded cable. The data-sheet also shows you what to do in this case: Connect a resistor between the sensor output and the cable.

For better performance you could convert the sensor signal into a balanced signal near the sensor and convert it back into a single-ended signal near your micro-controller. Balanced driver chips for audio would likely work well for this. If you do so, driving cables that long won't be a problem, even in noisy environments.