That's a question that most low-carbers have asked one time or another and in my experience this will differ from person to person depending on several different factors such as activity level, age, sex and your overall health. For instance someone with a metabolic problem will most likely lose at a slower rate and may also need to drop their carb levels to a lower level than a more active person.
I personally am not all that active but can still lose at a fairly decent pace when keeping my carb levels below 80 grams a day. Something else that you also need to consider when trying to lose weight is your sugar grams. For the most part I almost never eat sugar, but you will find that in a lot cases sugar can be hidden in the foods that you consume and that isn't even counting the natural sugars that you will find in fruits and certain vegetables.
For me keeping sugar grams under 16 or even lower a day seems to work best for weight lose, This may seem a little hard at first but I've found that it works pretty good for me and it's rare that I have problems with sugar cravings, unless I'm trying to recover from a cheat day such as a birthday or holiday.
Everyone is different and what works for one person may not work for another, which means that you may have to do a little experimenting to find what works best for you. But then again that's what life is all about.
If you're looking for some guide lines then you may find the following chart to be a helpful starting point.
100-150 grams a day - generally this work will for someone in a maintenance phase.
50-100 grams a day- most people will enjoy effortless weight loss in this range.
0-50 grams a day - extremely fast weight loss works well to help jump-start your weight -loss but hard to maintain over time. These levels may also work well for someone with diabetes.