I am so sorry for your loss.
The decision to humanely euthanise a beloved doggy best friend is always the toughest thing in the world..I had to do it once and would rather gnaw off my arm than have to do it again. :-(
I know you did the right thing though, cancer can be painful and devestating..esp to an active animal like a lab.
I send big hugs your way, and please, I know others will act like it is nothing and you should get over it quickly...but don't, you mourn just as long and as hard as you need to..otherwise the pain will never really heal. (I have mourned my 2 babies for year-and am feeling better but still not 100%)
As to what happens to them...that depends on your individual belief system...
some believe they go to heaven
some believe they go to some kind of limbo waiting for you to meet them again some day.
some believe they will re-incarnate as another beloved pet in your life.
I say, believe whatever makes you feel best...even if it isn't true..you have no way to know..so you might as well believe it with all your heart.
My personal belief is that once someone is gone, that is it..they are just gone (like sleeping, only longer)...and the rest of us are left to mourn and remember. But that is just my personal thing...each persons beliefs are equaly valid.
I lost by German Shepherd when he was run down by a truck and greived over him for a week.
Death is the only certainty to life. Like dogs, we all have to go one day...in some circumstance or the other.
Dont worry, your dog will now be where all good souls go. At least, you were humane enough to releive it of the suffering.