Babies should be baptized within a few weeks of their birth and infant baptisms are not forbidden during Lent. Here are the relevant canons from the Code of Canon Law
Though baptism may be celebrated on any day, it is recommended that normally it be celebrated on a Sunday or, if possible, on the vigil of Easter (canon 856; emphasis added).
§1 Parents are obliged to see that their infants are baptized within the first few weeks. As soon as possible after the birth, indeed even before it, they are to approach the parish priest to ask for the sacrament for their child, and to be themselves duly prepared for it.
§2 If the infant is in danger of death, it is to be baptized without any delay (canon 867; emphasis added).
I recommend that you take these canons to your pastor and request baptism for your child as soon as it is reasonably possible after the birth, even if that time falls during Lent. If he refuses, seek out another priest. If you are unable to find a priest who will perform the baptism during Lent, I recommend contacting your diocese for a recommendation. If that doesn't work, please contact the St. Joseph Foundation
for further assistance.