The Unwanted Calls
Answer: When the Torah warns us against lying it does not say "Don’t lie!" but rather "Distance yourself from lying". This phrasing is intended to warn us against prevarication of any sort, regardless of how much you can find justification for it. (The one exception is saying a "white lie" in order to preserve or restore peace between mates and neighbors.)
If it is your child that you instruct to lie about your not being there you have compounded your guilt by setting a bad example which the youngster is likely to emulate in other situations.
What then can you do?
If it is studying Torah that you wish to do it is in any case preferable to do so in a local Beit Midrash where you will not be disturbed by phone calls. When spending time with the family at home, in order to avoid these "nuisance calls," either remove the receiver during that special period, or request that whoever answers the phone inform the caller that you are not available at that moment (which is true!) and invite them to call back at an hour which you have previously designated as the time you are prepared to receive calls.
The important thing to remember is what the Sage Rav told his son when he caught him lying to his mother for the noble purpose of assuring that she would prepare the sort of meal for her husband that he desired rather than continue her practice of ignoring his wishes. The son was always the go-between, relaying to his mother his father’s menu wish. When he grew older and realized that his mother was spitefully preparing meals opposite to his father’s instructions he hit on the idea of switching the instructions. When Rav surprisedly came home that day to a meal he really wanted he discovered what his son had contrived. He praised his ingenuity but scolded him for indulging in falsehood, which is so habit-forming that it twists the tongue of its perpetrator and makes it difficult for him to ever adhere to the truth.
