Having the block sleeved is neither a minor nor cheap procedure. In terms of not blowing up the motor, the stock block is fine as long as you make sure it's in good shape (i.e. pulls good numbers on a compression/leakdown test) and all of your maintenance has been taken care of.

To get a turboed LS motor to 240 at the wheel however, will require more than just bolting on a turbo kit. That will net you around 200 at the wheel. You'll need a boost controller, an electronic means of tuning your air/fuel mixture, higher flow rate fuel injectors, an upgraded fuel pump, a nice 3" Thermal R&D exhaust and some dyno time getting it all dialed in.