on the same basis of calculation as above $300m values the...

Assuming using your market cap of Lith Coy at $200m ( basically represents 25c per share at current levels) values the project at $400m with the partner putting in the capital to build the plant for 50% equity.
The theoretical share price calculation of Lith Coy will look something like this
1 LithiumCo to 8 FFX shares= 102m shares represents $2.00 per share
The capital raising of $48m will need to be at $2.00 per share because thats the market value
therefore a total 126m shares on issue should have a theoretical share price of @$1.60 per share on listing Or in current terms 20cents per share

on the same basis of calculation as above $300m values the project at $600m with the partner putting in the capital to build the plant for 50% equity with $100m for working capital or whatever. Lith Coy would then need to raise $100m at $3.00 per share.
therefore a total 135m shares on issue should have a theoretical share price of @$2.20 per share on listing Or in current terms 37 cents per share