| Rav Baruch Fried
Answer: This is a unique case of Hashavas Aveidah in the sense no item is being lost; rather, an expense is being incurred. It's worth noting that cases like this are often in the category of aveidah m'daas, because people often are aware of things like this and simply don't care. If it is known to be a case of aveidah m'daas, you don't have to mix in.
If, however, it appears to be a situation where the neighbor forgot to turn off his outdoor lights, this would fall under the category of "aveidas karka". The Gemara derives from a pasuk that if floodwaters are surging toward someone's field, an observer is obligated to make a fence to dam up the incoming water in order to save his friend's field. No item is being lost in this case, but one still has an obligation of Hashavas Aveidah to prevent a future loss.
This rule would apply in the case in question as well. The Aruch Hashulchan says that aveidas karka applies to all forms of loss, and one should get involved to save his friend from any such loss.
This specific case is a little more complex because one could argue that every second of light is worth less than a perutah, which is not obligated in hashavas aveidah. I think that common sense would dictate that this is an ongoing loss of money and one would be obligated to inform his neighbor that his lights are on in order to save him money. | 
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