I just started low carb and am wondering how it will effect my lifting weights and running? I lift weights 4 days a week and run 2-3 miles 4 days a week. What is the least amount of carb intake for my lifestyle?

Least amount is zero. You may feel easily fatigued at first, but will likely get over it, especially quickly for the weightlifting.

Will there be any muscle and strength loss?

I'm assuming you are trying to lose about 15 pounds right? When I wanted to lose a similar amount I tried a more standard diet and lost so much strength that I couldn't do any more pullups at 155 than I could at 165. A year later I did it again with a ketogenic diet. That time as I dropped weight the number of pullups went way up. So I have to conclude that the ketogenic diet was muscle sparing, but the standard diet was not.

I really don't know about cardio though. LC doesn't seem to hurt my performance, but I don't do it competitively and I didn't do a before/after stopwatch type comparison. I do know that I CAN run or rollerblade without feeling weak. I've heard many opinions on this board and lets just say different people report different results. But whatever difference there may be is likely to be modest.

If you are worried about losing lean mass make sure you are getting PLENTY of protein. Starch is not necessary for post work out benefit, but some very serious athletes feel better if they consume a small starchy veg after work out. You should check out Robb Wolf's paleo/cross fit info, he does a GREAT podcast that gets really deep into all the science as well as practical fitness applications of lowcarb/paleo.

I eased into low carb over a period of a couple of weeks so it was fairly easy. It seems that the people that struggle switching over are those that rush into it.
I eat very low carb. I do not run out of energy during workouts like I did when I ate a fairly typical bodybuilding style diet. I also don't need to try and fit the workout in between the every 3 hourly feeds that I needed back then. I'll just eat 3-4 times per day now which leaves plenty of time to fit a workout in between somewhere but now I usually workout on an empty stomach before breakfast anyway which is something I couldn't always do before going low carb.
I don't do any running though but have read several people say they got on fine with running and low carb.

Is a protien drink ok. 3 carbs, 2 grams sugar per serving.

protein drinks are for high carbers who are thereby deficient in protein. those who do low carb and eat lots of meat do not need protein supplements.

I can't imagine needing a protein drink while on a low-carb diet. Isn't that what steak is for?

It's fast and easy. It depends on your lifestyle. I work part time, so steak it is. But earlier in the year, I was out of the house for 10-11 hours for work and then out for another 1.5 hr for the gym AND another .5/hr at home workout. That left little time to cook, and protein shakes worked well for me at that time.

If you are looking to grow muscle and lose fat consider the anabolic diet. You remain in ketosis but you get regular floods of carbs to allow your body to build muscle (it is needed for that process).

I'd say just make sure you're getting your electrolytes in, and see what happens. All that exercise plus potassium/sodium wasting from the diet change=bad.

I'm a little agnostic about cyclic ketogenic diets. It's harder to build muscle on a lower-calorie diet, increased appetite during the carb-up is a possible confounder. Traditional Inuit didn't look like professional bodybuilders, but they did manage to have muscles. It's sort of a hard thing to prove. A three-month study might show greater increase in muscle mass with a high-carb diet vs a low-carb diet, but it might take a longer-term study to see at what point the two eating groups muscle mass plateaus. It's also kind of hard for people to act as their own controls in this sort of study, once they've gained muscle on one regime, they're just plain different. I guess the next best thing would be an identical twin study.

Jeff Volek's done a few studies, one with men and one with women. He found that it was possible to gain muscle on a low carb diet. I think that was in untrained individuals. I can't find the actual studies right now, they're not on PubMed.

I've considered going on a cyclic ketogenic diet, but years of eating very low carb has left me with very little appetite for carb.

Protein shakes are highly over rated, a very small amount of red meat, some eggs will cover all your protein needs.

As far as strength goes with my personal experience and low carbing, i got many issues, when i got into ketosis and depleted almost all my glycogen i did have huge issues with pumps, strength and i did fatigue a lot faster.

I cannot get used to the ketosis effect, note that not everyone is the same. Guy at my job did the protein diet for 3 months he said the first 3 weeks where hell but after that everything was fine, btw he is a soccer player, went from 226 to 183 and did not gain anything back.

This time around i will be looking into a better low carb diet, with some lean meats, like bison meats, calf liver, eggs, olive oil and soon to add coconut oil, some nuts very small amount, low carb soya milk and small amount of tuna.

I sort of put the butter, most saturated fats, bacon, sausage, out the window, because i feel they don't really have any benefits.

I also added black strap molasses 1 table spoon a day this stuff is like magic and 1 cup of mix frozen berries.

This way i can make sure that i never really reach ketosis, to be honest most studies i read said that ketosis might not need to be reached for weight loss.

I am also combining this semi-low carb diet with intermittent fasting so i eat twice a day and try to fast for at least 15 hours a day.

Intermittent fasting is a very good option to had to any kind of diet, its free and does wonders for the body.

Anabolic diet is a great program and part of the best out there with CKD and UD2.0, bodyopus

I am following the Anabolic Diet now. So far so good. I do HIIT and strength training all week...rest on the weekends.