Was Reish Lakish a talmid of R'Chiya to say this?
Was it within the 12 chodesh? See Y"D 240 (?) Hilchos Kavod Ravo and the Bair Hatev about how long there is to say HK"M.
RAV YAKOV EMDEN addresses your questions. He writes that Reish Lakish lived after Rebbi Chiya (Rebbi Chiya's son, Chizkiyah, was a teacher of Rebbi Yochanan, Reish Lakish's contemporary). Rav Yakov Emden says that Reish Lakish used this phrase of "Hareini Kaparaso" out of his great love and admiration for Rebbi Chiya, even though he never learned under him, and even though he was not speaking within twelve months after Rebbi Chiya's passing.
The TASHBETZ (1:122) preceded Rav Yakov Emden with your question, and adds that it is not even permitted to use the words "Hareini Kaparas Mishkavo" after 12 months. It is disgracing the Rebbi to assume that he is suffering Din Shamayim even after 12 months. He explains that Reish Lakish did not say "Hareini Kaparas Mishkavo ," which would imply that he is accepting the Din Shamayim that occurs immediately after death. He left out the word "Mishkavo" intentionally; without saying "Mishkavo" one may say "Hareini Kaparaso" any number of years after the passing of a Rebbi (or a Rebbi's Rebbi).