I lived in Almancil for 6 months and know the area well.
There is essentially no regular public transport between Almancial/Vilamoura/Loule/Quarteira and Vale de Lobo apart from Taxis.
Be aware that if you holiday there without your own transport you will be stuck "on-site".
Also be aware that taxis to and from even Almancil will be expensive as VDL is actually at least 8 kms from Almancil.
Strongly recommend that you hire a car.
If you are coming in from Lisbon, I recommend you consider picking up a car at Lisbon Airport and driving or else train/fly to Faro and pick up a car there. There are no car hire depots near train stations in the Algarve except in Faro. (Europcar/AVIS)
As Fletch55 said see Cubsur's site.
The following may also be useful:
http://www.solpraiaferias.com/index.php?content=cheg_en
http://barlaventostravelblog.blogspot.com/2007/05/lisbon-to-olhos-dagua.html
