In terms of liturgical law, the priest makes the choice in who does the ministries. The exception is if someone has been instituted as a lector, (using the ceremony of institution, usually by a bishop). Perhaps this is part of the reason that so few lectors are instituted.
From the 2002 General Instruction of the Roman Missal (GIRM) approved for the USA, which can be accessed from
romanrite.com/girm.html :
“99. The lector is instituted to proclaim the readings from Sacred Scripture, with the exception of the Gospel. He may also announce the intentions for the Prayer of the Faithful and, in the absence of a psalmist, proclaim the Psalm between the readings. In the Eucharistic Celebration, the lector has his own proper office (cf. below, nos. 194-198), which he must exercise personally.
Other Ministries …
101. In the absence of an instituted lector, other laypersons may be commissioned to proclaim the readings from Sacred Scripture. They should be truly suited to perform this function and should receive careful preparation, so that the faithful by listening to the readings from the sacred texts may develop in their hearts a warm and living love for Sacred Scripture. …
104. It is fitting that there be a cantor or a choir director to lead and sustain the people’s singing. When in fact there is no choir, it is up to the cantor to lead the different chants, with the people taking part. …
107. The liturgical duties that are not proper to the priest or the deacon and are listed above (cf. nos. 100-106) may also be entrusted by a liturgical blessing or a temporary deputation to
suitable lay persons chosen by the pastor or rector of the church. All should observe the norms established by the Bishop for his diocese regarding the office of those who serve the priest at the altar.”
The “temporary deputation” is temporary. The pastor can end it without needing to give much of a reason. For example, he has a dream and the angel Gabriel tells him not to allow someone to be a lector. A person is too old or too young. The are too many women or men. Someone will not sign a document. etc.
I have been instituted as a lector, and feel a strong case can be made that failing to use an instituted lector when available is not following liturigcal laws. The case was made through a church tribunal in 2000. It was unsuccessful, but I think would be more likely to suceed today, with the 2002 Roman Missal having been published. The case can be read about at
romanrite.com/Tribunal.html .