Brother Salman, I know exactly, that the word "Tahlil" doesn't originate from Turkish, it has an Arabic origin. According to the vowel harmony rule in Turkish "A" and "I" vowels can't be in a single word. (in original Turkish words) I hope that's helpful.

تهليل is completely an Arabic word . It's the noun(masdar) from the verb هلّل , it means applause or crying joyfully. It has another meaning too : هلَّلَ المُسلم تَهلِيلًا وسبَّح تَسبيحًا it means : "The Muslim said (la ilaha illa Allah) لا إله إلا الله and said (subhana Allah) سبحان الله