The takeover over Lex's business ventures would be fairly easy - Costmart and Price House would be part of a larger parent company with lots of money.
Lex's companies were part of a larger corporation as well, with Lex as the majority stock-holder. With Lex out of the picture, the voting rights to his stock would devolve onto whoever the company papers or the courts indicate. That person would then be in a position to be forced to divest (sell the stocks, probably at a major loss) to the parent company of Costmart.
In general, a hostile take-over occurs when enough of a company's stocks can be bought up to make the outsider a majority stockholder - without making an open offer to buy the company to the company's governing board. The takeover can be quiet - using third parties to get the stock before anyone realizes it's one person or company buying everything up.
As for Intergang taking over Lex's operations - murder, blackmail, etc.