This example makes sense, as we can replace Lucie et moi with nous:
Lucie et moi allons au cinéma tous les mercredis.
However, in everyday spoken French, most people use on for the first person plural as the conjugation is easier (eg: On va au cinéma), where the conjugation takes the form of the third person singular. Given this, can we also use the third person singular conjugation here? That is:
Lucie et moi va au cinéma tous les mercredis.