There are limits on the percentage of shares one may acquire without public disclosure of further intentions - I think that's 5 percent in this country, 10 percent in Canada, but I'm not too sure.

Anyway, what do you think would happen to the LBSR share price, if, say, Rio Tinto announced they had acquired 5 percent of the shares and intended to buy more?

In my opinioin, therefore, no one is going to buy out this company for as little as your scenario suggests. Besides, and as you pointed out, a sale would have to be approved by shareholders, and it's not likely that the majority of holders would approve such a transaction. Again, that's opinion, but I think well founded.