From the WLC...

Question 156: Is the Word of God to be read by all?

Answer: Although all are not to be permitted to read the Word publicly to the congregation, yet all sorts of people are bound to read it apart by themselves, and with their families: to which end, the holy Scriptures are to be translated out of the original into vulgar languages.

This should be understood in light of the what the divines said in the Directory for Public Worship

Of Publick Reading of the Holy Scriptures.

READING of the word in the congregation, being part of the publick worship of God, (wherein we; acknowledge our dependence upon him, and subjection to him,) and one mean sanctified by him for the edifying of his people, is to be performed by the pastors and teachers.

Howbeit, such as intend the ministry, may occasionally both read the word, and exercise their gift in preaching in the congregation, if allowed by the presbytery thereunto.

The Reformed understanding is that the reading of God's word belongs to the ministerial office.

__________________
Rev. Adam King
Minister without a call (WPCUS)
Stated Supply: Reformed Presbyterian Church
Sterling, KS