A full list of primary and secondary schools in Lagos can be found here:
http://www.cm-lagos.pt/portal_autarquico/lagos/v_pt-PT/menu_turista/concelho/educacao/escolas/
The ESCOLA SECUNDÁRIA COM 3ºCICLO DE GIL EANES & ESCOLA SECUNDÁRIA DE JÚLIO DANTAS are the two secondary schools in the town.
The Escola das Naus behind the Marina may also be of interest.
http://www.eb23-n2-lagos.rcts.pt/
Be aware that all of these are Portuguese State Schools. I would suspect that at least some of the head teachers will have some English, but do not count on it. Whether they can provide extra tuition I don't know. The state education system here is currently under great pressure so don't count on it.
I would suggest that in the first instance you contact the Escola das Naus.
