Can a Catholic funeral be held on Holy Thursday?
No, funeral Masses are not permitted on Holy Thursday.
General Instruction of the Roman Missal:
380. Among the Masses for the dead, the funeral Mass holds first place. It may be celebrated on any day except for Solemnities that are holy days of obligation, Thursday of Holy Week (Holy Thursday), the Paschal Triduum, and the Sundays of Advent, Lent, and Easter, with due regard also for all the other requirements of the norm of the law.