The best way to reach Algarve from Lisbon is by Private Transfer.
From Lisbon, you can request pickup at your hotel/accommodation front door, or airport, with your luggage, directly to your destination in Algarve, without the hassle of public transportation and crowds.
Any destination place in the Algarve can be covered, some examples: Lagos, Sagres, Lagoa, Faro, Lagos, Quarteira, Quinta do Lago, Carvoeiro, Almancil, Albufeira, Portimão, Tavira, Vilamoura, Salema, Ferragudo, Porches, and much more.
There are three options to consider:
OPTION #1: Direct Transfer (Private), no stops (by LisbonGuide / Concierge Portugal): https://lisbonguide.org/private-transfers-portugal/
OPTION #2: Private Transfer, by Portugal Magik Tours: https://portugal-magik.com/tour/private-transfer-from-lisbon-to-algarve/
OPTION #3: Car + Driver at your disposal with Portugal Magik: https://portugal-magik.com/destination/algarve/
You can also follow here this app, for instant quotation and booking: https://lisbon.ridebitsapp.com/central/new_reservation
Enjoy Lisbon and Algarve. Make sure to travel in comfort and safety.
Gonzalo
Founder/Owner of The Lisbon Guide, one of the major blog references in Portugal, established in 2014 and receiving every year 250.000 visitors from all over the world, looking to provide the best experiences in Portugal. In partnership with Portugal Magik for all private tours and transfers across Portugal, Gonzalo loves a good seafood meal at Monte Mar Cascais, and all from Michelin Chef Avillez. Favorite Hotel in Lisbon/Portugal, Penha Longa Resort by Ritz Carlton.
For over 15 years, Gonzalo have been helping thousands of travelers yearly to plan a perfect trip to Portugal. Based in Lisbon/Cascais and working in this field for over 20 years, with multiple ongoing projects. Also an avid TripAdvisor user level 6 with more than 300.000 readers worldwide.
Many years working also as a Private Guide of Lisbon, Sintra, Fatima, Porto, Douro Valley, Evora, and other locations in Portugal.