I plan to sous vide lamb chops, which is going to take 3 hours. Since I have to work, it will be too late for dinner if I start cooking after work. Can I sous vide it for 2 hours the night before, put it in the fridge, and continue cooking for another hour the following day? Do I need more time on the following day as the temperature of the meat is lowered in the fridge?
No, you will need to cook it for the proper length of time all at once.
Sous Vide heats the food very slowly and depending on the density and thickness of the food, it can take quite a while for the center to come up to the finish temperature. Additionally, this temperature is usually lower than the temperature applied in other methods of cooking so it kills bacteria and parasites more slowly than high-temp cooking.
For proteins, an extended cook time is needed to get the center up to temp. Additionally, because the temp is lower, more time is needed at that temp to kill off any bacteria or parasites.
By not heating for the entire time at once, you risk never bringing the center up to temperature! It might be undercooked or worse, it might be dangerous.
Note: Some fatty proteins are cooked at a higher temperature for longer periods of time to also break down collagen and connective tissue. Not cooking them all-at-once will similarly not have the desired effect on the collagen and connective tissue.
Another Note: Some might wonder how anyone ever cooked and served a rare roast beef in the past if a long exposure to lower temp is needed to make the roast safe in the center. The answer is that contamination of beef with parasites is not common and even though beef does contain bacteria, the bacteria exists near the surface of the meat. The density of the meat makes it difficult for the bacteria to spread to the interior parts. This keeps the center perfectly safe to eat raw if you could somehow cut off the surface without inadvertently contaminating the center with bacteria from the knife.
One solution is to cook the protein completely on a day when you do have the time. You can leave the lamb chop still in the vacuum bag in the fridge for a day-or-two and then drop it back into the water bath at the same temp on the day that you want to serve it. Because you have already killed all the bad stuff and it has remained sealed, all you need to do is get the center up to temp and it will be ready for the final searing step or serving.
That solution is not perfect however. Empirically I have observed that when using this method some meats will dry out quickly on your plate after slicing. It must be something with the proteins or cell structure so that it releases all of its water quickly after being sliced. I've mostly experienced this with leaner meats like beef chuck steaks. I haven't tried it on lamb chops, but they are similar in leanness to a chuck steak.
Sous vide lamb chop should only take you about 1hour and 30 minutes @ 131F (55C). This will result in a medium rare chop. Given your 2 hour time window, I would cook for the 1.5 hours, then chill in ice bath and refrigerate. You could even freeze at this point. Anyway, re-therm when you want to eat. It will take about an hour - 1.5 hours. I would reheat a couple of degrees below your cooking temperature so as not to overcook.