Is HH Dalai Lama conceited? I heard that Theravada presupposes HH Dalai Lama is not even reached initial bodhisattva enlightenment and that His existence is mocked. Is it not so?
Its often best to avoid comparing Theravada to Mahayana.
For example, in Theravada there is no notion of 'bodhisattva enlightenment'. In Theravada, the word 'bodhisattva' is never used, apart from referring to Gotama prior to his Awakening. For example, in the Pali suttas, there is the stock phrase:

Bhikkhus, before my enlightenment, while I was still only an unenlightened Bodhisatta, it occurred to me:...
https://suttacentral.net/mn19/en/bodhi

As for HH Dalai Lama, his former political role as leader of Tibet is somewhat alien to Theravada monasticism. Therefore, occasionally, Theravada people criticize the Dalai Lama; including for some of his political decisions &amp; actions.
This said, if HH Dalai Lama has inwardly realised not-self (anatta) &amp; eradicated identity belief (sakkaya ditthi) then he has reached one of the four levels of enlightenment according to Theravada. Personally, I believe he has enlightenment.