Public transport in St Lucia is pretty good depending on where you live in the suburb. Buses services most of the suburb and if you live near the river then you also have the CityCats (ferries) as well. When I lived in St Lucia I actually got rid of my car because I used the buses and CityCats to get to work in the City. The nearest train station is at Toowong and you can get a bus there for trains for destinations past the CBD. Check out the journey planner at www.translink.com.au for an answer specific to the street that you live in.