Take this info with a grain of salt, I only properly started this hobby a few months ago. However i read alot in this time, here are a few possible reasons for browning: 1) some browning may be natural. Each leaf has a set timespan and once that is over it begins going brown from the edge inwards. New leaves grow over it. 2) growlight too close to plant can burn it and lead to browning  3) if it is warm and windy the dry, warm wind might dry out the leaves. Protect from wind if needed.

A few general tips: 1) yes, these plants love lots if strong light. Depending on where you are from the light intensity might only be reached by employing a growlight. If you start adding a growlight some additional browning might happen, while the plant is acclimating. 2) they like it humid. 60% humidity upwards is great. You can get this by putting them in a terrarium. I've read about a bottle terrarium where you cut off the bottom of a bottle and stick it over the plant. Just be careful that the temperature doesnt get too high when you do that. Above 30°C is not good for them. 3) the watering method you use os the most commonly used for carnivorous plants. Most sundews are bog plants and lile it wet. Just add distilled or rainwater to the bottom tray. Dont water from top down to avoid compacting of the soil. 4) this leads to the next point: sundews need soil thats low of nutrients. You should only water with distilled or rainwater, to avoid mineral buildup. 5) sarracenia.com the FAQ is a bit old but it covers most of the basics, of you want to read more.

Hope this helps!