With regard to adults who have not received Christian baptism, the **Rite of Christian Initiation for Adults (RCIA) **states:
“the third step: having completed their spiritual preparation, they [catechumens] receive the sacraments of Christian initiation” (no. 6)
“The third and much shorter period, which follows the rite of election, ordinarily coincides with the Lenten preparation for the Easter celebration and the sacraments of initiation.” (no. 7, emphasis added)
“…the Easter Vigil should be regarded as the proper time for the sacraments of initiation. Because of pastoral needs, however, ***the sacraments of initiation may be celebrated at other times ***(see nos. 26-30)” (no. 8, emphasis added)
“The entire rite of Christian initiation is normally arranged so that the sacraments will be celebrated during the Easter Vigil. Because of unusual circumstances and pastoral needs, however…the sacraments of initiation may be celebrated at a time other than the Easter Vigil or Easter Sunday…preferably [choose a day]…during the Easter Season to celebrate the sacraments of initiation” (no. 26. emphasis added)
That’s a common misconception–that baptisms are not allowed during Lent. There is no such restriction. Again no restriction (other than Good Friday & Holy Saturday). In fact, the Church says precisely the opposite, that baptism should occur as soon as reasonably possible.
It might be pastorally sound to schedule a baptism on Easter Sunday or wait until the Easter Season. Let’s say that the parents request baptism on Palm Sunday and the pastor says “well, I can do it then, but would you consider waiting a week and having it on Easter Sunday instead? Here’s the reason…” That would be fine, but a pastor cannot outright refuse to do a baptism during Lent. He has an obligation to provide the Sacraments whenever a reasonable request is made.
Although some priests might ask someone approaching for baptism to wait because Palm Sunday is already a pretty busy day for them, there is no canonical reason why the sacrament can’t be celebrated that day.