If you book now the fastest and cheapest way may be by low cost flight
Valencia - Madrid
try Spanair
www.spanair.es
and then
Madrid - Faro - daily.
www.ryanair.com
It looks like the flight Madrid - Faro on that day is full but the day after is still available.
Prices look very good.
If you caught the early morning spanair flight from Valencia you should connect with the Faro flight.
From there you can either, taxi, shuttle or bus/train to Lagos.
It will still take most of the day though.
Alternatively you are looking at:
Valencia - Seville
Vueling Airlines
www.vueling.com
and then bus to Lagos
or bus all the way.
valencia - seville
seville - lagos.
You may find more useful info and links on the following sites:
http://www.solpraiaferias.com/index.php?content=cheg_en
and on my blog where I keep also sorts of posts on transport to and from the Algarve.
http://barlaventostravelblog.blogspot.com
