Does solving chess puzzles help in overcoming laziness? I lost many games in a tournament because I am too lazy to calculate variations, e.g.: calculating 4-5 moves deep when defending to be sure that I will not be down in material.
From personal experience doing puzzles has no effect on my level of laziness. What it does, which is more important for me, is widen my thinking. I become less narrow in the possibilities I will consider simply because I have seen unlikely moves work in the puzzles I've tried.
Overcoming laziness is more a problem of motivation, will and energy.
Tony Miles used to tell the story of when his doctor prescribed beta blockers for him for a medical problem. In his next tournament he lost the first three games. Although this was bad enough it was not what really worried Miles when he tried to work out what was going on. The problem for him was that he was losing and he just didn't care. He blamed the beta blockers for this and stopped taking them with the result that he started caring more during the game about his position and so started winning again.
Doing puzzles makes you more alert to tactics, and usually this allows you to calculate more quickly. But you need to think about how you have phrased your question: Consider the outside-chess question, "does increasing your intelligence make you less lazy?"
It does help to offset some of the potential problems you face in being lazy, but at the end of the day you need to be willing to work. In reality, doing puzzles gives you ideas and increases your tactical awareness over the board, but you still need to check that these ideas work over the board when some things have changed slightly.
There is also a mindset issue: when you spend hours in preparation for a tournament, studying opening theory, middlegame strategies/tactics and endgame theory, why are you willing to cast it all aside to save yourself from the pain of spending a few minutes to just think over the board? It's much like a student who studies exceptionally hard for a math exam, learning little calculation tricks left and right but is unwilling to double check his answers on the day of the test.
It's similar to @Brian Towers how solving puzzles improved my play: in regular looking positions I started coming up with a target at least, how I can modify the position and with a bit of luck turn it into one where I can make a non-straightforward move, possibly a sacrifice, and gain advantage. It widens your perspective and gives you additional goals to aim at during the game. Even if you're not a tournament player, this all makes your games more fun.
Laziness is not a problem that can be solved by solving more puzzles. Solving more puzzles will help you widen your thinking and solving the right puzzles for you (puzzles which require in depth analysis) might help you improve your chess but it would not help with laziness.
The real question to ask yourself is whether you are too lazy to think and can do it in extreme situations, or you are unable to think through all the situations and assume it is laziness. If it is the latter case, then puzzles will help but if it is the former, then puzzles will not help much.