I am so sorry to read you had to euthanise your 13yr old best friend. I empathise totally with you. In fact, my current situation is very similar. I had my own dog, BB (a lurcher), and my partner had his own dog, a mixed breed called Giro who was 6 yrs younger than BB. My partner and I have been together 5 yrs and by pure luck both dogs not only got on with each other but became the very best of friends. They spent more time playing with each other than they did with me, which was fantastic and a joy to watch. BB was more dominant and often dictated what Giro should do, even though he was younger and more able to be 'in command' as it were.
BB sadly became very ill very quickly (kidney disease) and shortly after her 12th birthday in November last year, we had to help her to go over the rainbow. We were devastated by the loss.
Giro was certainly affected by it. He did things he would not ordinarily do, such as sit for hours in the hallway near the front door, as if waiting for her to return. He eventually adapted, and is now more or less back to his old self, though he is slightly more clingy and sleeps outside our bedroom door rather than downstairs as he used to do.
I think the article link given by Caryopteris is very well worth reading. It puts in a nutshell what happens to dogs and how some of the traits of grief might be misinterpreted by owners. For the most part, dogs operate under a hierarchy system and live largely in the moment. The loss of a pack member will certainly affect them, but they are more likely to react adversely to the pack leader's (that means you) change in behaviour. As far as possible, try to keep things as normal as possible for your lab, although you might want to give him extra walks and a little more attention over the next week or two, just to reassure him that things are okay.
Being alone in the house may be an issue, but it is probably better to wait and see if that happens. On the other hand, he may be absolutely fine. Have you considered getting him another companion? This may be the answer to any boredom 'acting out' behaviour long term, but it's early days yet. Tony
From Cesar Millan's site:
http://www.cesarsway.com/cesarstips/problembehaviors/Dealing-with-Grief