According to canon law, only laymen can be permanently installed as lectors:
Can. 230 §1 Lay men [Latin, *viri
] whose age and talents meet the requirements prescribed by decree of the Episcopal Conference, can be given the stable ministry of lector and of acolyte, through the prescribed liturgical rite. This conferral of ministry does not, however, give them a right to sustenance or remuneration from the Church.Any layperson, male or female, can serve as a lector by temporary deputation:
Can. 230 §2 Lay people can receive a temporary assignment to the role of lector in liturgical actions. Likewise, all lay people can exercise the roles of commentator, cantor or other such, in accordance with the law.
Paul’s injunction in First Corinthians (14:34, not 15:34) is usually considered to be a disciplinary measure. This understanding is based upon 1 Cor. 11:5-13 where the apostle Paul assumes that there are circumstances in which women speak in church:
But any woman who prays or prophesies with her head unveiled brings shame upon her head, for it is one and the same thing as if she had had her head shaved (v. 5).
This passage is part of a section on problems in the liturgy in the churches in Corinth, so we can deduce that Paul is working with the assumption that a woman is praying and prophesying during the liturgy. If that is the case, then he obviously doesn’t expect a woman never to speak in church, only to follow a disciplinary injunction that he has given. Disciplinary injunctions are changeable, so later generations of properly-constituted ecclesial authorities could allow women to serve as lectors.