Hi Jean,

Stictly speaking -

Un liseur or une liseuse is someone who loves reading  as a hobby.

e.g. C'est une grande liseuse de romans = She is an avid reader of novels

Un Lecteur or une Lectrice can be someone who is paid to read out loud

(delivering a lecture ) or the term is used for the formal readership of newspapers, magazines etc...

e.g.  'les lecteurs d'un journal, ou d'un hebdo " 

Hope this helps!