I'm Hi Anthony,
All meteor showers are tricky in light polluted skies. Most meteors are faint and the light pollution either overwhelms them or makes it difficult to spot them.
With the Lyrids, or any other shower, it isn't 100% necessary to actually see the constellation itself. The name of ALL showers is given because all the associated meteors all appear to radiate from a given constellation. So the Lyrids, there may appear meteors dead overhead, but if you draw a line along the path the meteor took, it will lead to the constellation Lyra that for us in Australia is a horizon hugger.
Your best bet will be to find a location that will give you the biggest sky possible towards the north, but with the least amount of bright lights towards the north.
A couple of suggestions would be South Head or Christianson Park in Vaucluse, or Shelly Lookout in Manly. These are along the coast. If you can avoid looking through the CBD or other major lights in you local area, that will be as good as any other place that isn't outside of Sydney.
Just be aware that a meteor rate of 20 an hour is very low, and will test your patience. And this will be a mix of faint and only the occasional brilliant flash. That article you put a link to is very light on that aspect. Few meteor showers are especially spectacular at the moment. The two associated with Halley's Comet are probably the best at the moment, the Orionid and Eta Aquarid meteor showers. But even these are a little light on meteors as the comet's last appearance was many years ago and there associated dust is now thin. The Leonids can also throw up the occassional surprise rate and a couple of others.
Happy meteor hunting!
Alex.
PS: the best gear to use for meteor spotting is your own eyes! Binos or telescopes are pretty much useless here as meteors appear all across the sky and are so short lived you cannot move the scope and look into it in time.
This is not to say not to take binos or a scope, but you won't be able to see meteors while looking through them, but you will be able to do something in between patrolling the sky.
You may like to take wide angle long time exposure photos as these may pick up meteors you may miss.
Alex.
