Help with powering LED strips from a LED TV
Does that mean each LED needs 0,17 Amps (0.5 Watts / 3 Volts)?


P = V * I &lt;=> 0.5 W = 3 V * I => I = 0.5 W / 3 V = 0.17 A

So, yes.


  How do I calculate the power requirements for the whole strip or both
  strips?


72 + 72 leds * 0.5 W = 144 leds * 0.5 W = 72 W


  Any recommended power supply / driver that supports dimming?


Use a power supply that has some headroom (more power than you need).
For dimming, I cannot give an answer.

However, as AndyAka says in his comment, you can better buy a new one, knowing the specs. From China, these are very cheap anyway.

Update

About the amperage … if the LEDs are 3 V, you should use a 3V power supply (although I never saw LED strips with 3V).

For the amperage, you can use P = V * I again:

72 W / 3 V = 24 A

And to have some headroom, use e.g. 30 A.

Actually this is really a lot, but 3 V is very low. You might even think about using some transformer from e.g. 24 V or 12 V to 3V and using a lower amperage.