Removing the holy water from the baptismal font during Lent is an innovation based on custom not liturgical law. The practice shows a lack of understanding of the season of Lent.
“Through its twofold theme of repentance and baptism, the season of Lent disposes both the catechumens and the faithful to celebrate the paschal mystery. Catechumens are led to the sacraments of initiation by means of the rite of election, the scrutinies, and catechesis. The faithful, listening more intently to the word of God and devoting themselves to prayer, are prepared through a spirit of repentance to renew their baptismal promises.” [Ceremonial of Bishops, #249]
For both catechumens and the faithful it is important to keep in the forefront of their mind the importance of the waters of baptism. Catechumens passing by the baptismal font are led to yearn for the day when they will be claimed as God’s children and join the family of God. The faithful passing by the baptismal waters are led to reflect on how they have been unfaithful to their baptismal promises and use the time of Lent to repent so that they are ready to renew those promises at the Easter Vigil. The waters in the baptismal font serve as a constant reminder to both groups.
There is no document that addresses this issue directly since it is the innovation of someone’s imagination. The only time that emptying the baptismal font is addressed is in the Ordo. In the directives for Holy Thursday the Ordo says: Holy water may be removed from all fonts. They are refilled with the water blessed at the Easter Vigil.