It wont kill all of them but should give you some peace of mind as it will kill the ones that are on the surface and hopefully you wont get any bites. We just got finished dealing with bed bugs and sprayed everything down with Lysol to start. But I recommend calling a Pest Control Operator to deal with the problem. If you can't afford one HOTSHOT Bedbug and Flea killer works well but take many applications. We are pretty sure ours are gone but are continuing to fog our house with hotshot. I use three cans in every room that way the room is saturated with pesticide. Wait about 4 hours then open all windows and doors turn on fans and AC to air out the building before resuming occupancy.
You might be able to kill a bed bug by spraying lysol directly on it, but simply using it on the mattress is not going to get rid of bed bugs at all.