Yes, one must sleep in order to perform Tahajjud prayers.

تھجد is derived from ھجد (hajada). ھجد (hajada) and ھجد (hajjada) and تھجد (tahajjada) mean the same thing i.e. (1) he slept or slept in the night or in the latter part of the night; (2) he remained awake or was sleepless or wakeful in the night; (3) he awoke from sleep to pray or for some other purpose; (4) he prayed in the night. Hence praying in the latter part of the night is called تھجد (tahajjud). (Lane & Aqrab).

Therefore, true ‘Tahajjud’, as per the Arabic language, means to cast away sleep and then stand up (to pray) – ‘Juhud’ means to struggle; signifying the struggle of getting up after sleep.

Therefore, the voluntary prayers that are a result of getting up after sleeping are called ‘Tahajjud’.

However, if someone, for some exceptional reasons, could not sleep and desired to get up and offer voluntary prayers, there is no restriction on them from the Sharia.