AKE is now an over $10B AUD company and LTHM is a over $5B USD so over a billion or so shares on issue for NewCo won't be a problem.
From what I can tell via a quick search, there are about 209,000 LTHM shares on issue, so after the merger there will be 209,000 x 2.406 = approx. 503,000 shares on issue. Plus there will be options etc etc so with AKE having about 637,000 or so, you're right, there will be well over 1B shares on issue. (503,000 + 637,000 = 1.14B.)
Edit: sorry, just saw some of the calculations above.