Start by estimating the accuracy of your temperature sensor and controller. You're going to need to do some comparisons with reliable thermometers for this step. I'm guessing you don't have any laboratory grade thermometers at home that have recently been professionally calibrated. (Who does, really?)
Start by finding two or three digital cooking thermometers (preferably different models) that seem trustworthy. Then calibrate your PID controller by measuring the temperature of a mixture of equal parts crushed ice and water. It should be 0 °C. While you're at it, use the ice slush to check the accuracy of the cooking thermometers you found. Recalibrate or replace them as needed. Finally, heat some water to around 60 °C (or whatever temperature your think you'll be using most often for cooking). Then measure the temperature with your PID controller and the cooking thermometers. That should give you a pretty good idea of how accurate your PID controller will be during cooking. (If you find that your PID controller is accurate at ice temperatures, but quite a bit off at higher temperatures, you likely need a new temperature sensor.)
Sous vide accuracy is frequently in the neighborhood of +/- 0.1 °C, but +/- 0.5 °C is often good enough. I'm not sure what "low accuracy" means, but let's say, for example, that you estimate your accuracy to be +/- 2.0 °C. In that case, simply raise the temperature setting by 2 °C to compensate for the margin of error. It might result in a different level of doneness than you want, but the food will probably be safe.
Take a look at Douglas Baldwin's A Practical Guide to Sous Vide Cooking. Not only does it have some excellent recipes for beginners, but it also has some great safety information. If the food is to be consumed by pregnant women, you don't just want it to be cooked. You want it pasteurized. The guide includes tables for looking up the pasteurization time for fish, poultry, and meat (beef, pork, and lamb). If the meat is starting frozen, add about 30 minutes to the cooking time. If a recipe's going to take too long, use the tables to adjust the meat thickness or temperature in order to reduce the cooking time to your preference. Keep in mind that your shouldn't start the timer until the food is in the water bath and the water is up to temperature. So, save time by heating the water first thing when you're ready to cook.
Anything you salt will firm up in texture over a period of time. I suspect that since you cooked these with seasonings and then chilled and left them in the fridge before reheating an eating they firmed up a great deal in the fridge.
If you check out this blind tasting conducted by Dave Arnold at Cooking Issues you'll find some more detailed info about this topic. The gist of it is that for cook-chill-reheat purposes you shouldn't salt the meat before searing. For cook-direct serve meals your just fine doing it that way.
http://www.cookingissues.com/2011/10/12/to-salt-or-not-to-salt-thats-the-searing-question/
Best Answer
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.
SOLUTION
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.