The correct option is
A his wife died
In the given sentence, 'since' indicates a point in the past from which 'He' has been lonely till now. Thus, we can conclude that something happened at a point in the past which made him lonely. Thus, the answer must contain a verb to indicate some thing happened and it mus be in the past tense to indicate that it happened in the past.
Option A is incorrect. 'many years' does not have a verb or a particular tense. Also, it does not indicate that something happened and that event made him lonely. Thus, it is incorrect.
Option B is incorrect. 'long time' indicates a time period and does not indicate a point in time in the past. Also, it does not indicate that something happened and that event made the subject lonely. Thus, it is incorrect
Option C is incorrect. 'his dead wife' does not have a verb to indicate something happened. Thus, It does not justify why the subject is lonely and is incorrect.
Option D is incorrect. 'his wife died' indicates that the subject's wife died at a time in the past and from that point he has been lonely. Thus, it indicates that something happened and because of that the subject became lonely. Thus, it is correct.