I have a feeling Luthor will shave his own head.
Pictures of him so far show a man with not just a full head of hair, but long hair. He's grown it purposefully to that length and it's probably as much part of his 'image' as his business ventures and corporate successes. Like many men who value their hair and grow it long like in days of old, he may also associate it with his virility and as a symbol of his masculinity. Intellectuals were also noted in days gone by for having long hair.
I'd hazard a guess that at some point in this film, Superman & Batman will overcome whatever Lex's devious plan is, and his true nature will be exposed to the world - not the saviour of Metropolis or whatever he's presented as, but the deceitful egomaniac he truly is. And I think in doing so, he will shed off whatever remnants of his old image are left - including his long hair.
It wouldn't be entirely different to how Walter White embraced his bald head in Breaking Bad - as part of his 'true' Heisenberg identity - even after his cancer had receded and he was able to regrow his hair.