The second sentence is incorrect ; it should be Il le leur lit. I found a diagram that sums up the order of the pronouns in French : http://users.telenet.be/palm-mar/Taal_FRA_cod_coi.htm. As far as I know, it is correct.

This topic has probably been treated several times on this forum.

When the indirect pronoun is third person (lui or leur) then the indirect object pronoun comes after the DOP. Otherwise, the indirect object pronoun comes before the direct object pronoun.

For example:

Il me le donne (He gives it to me)

Il le lui donne (He give it to him)