To solve the expression $15 - 4 \cdot \lvert -3 - 7 \rvert$, let's break it down step by step:

1. Calculate the expression inside the absolute value: $-3 - 7 = -10$

2. Take the absolute value: $\lvert -10 \rvert = 10$

3. Multiply by 4: $4 \cdot 10 = 40$

4. Subtract from 15: $15 - 40 = -25$

So, the final answer is $-25$.

Would you like details or have any questions about the steps?

Here are some related questions:

1. How do absolute values affect subtraction inside them?
2. What is the difference between $|x|$ and $-x$?
3. How do we simplify expressions with multiple operations and absolute values?
4. Can the absolute value of a number ever be negative?
5. What happens if we have variables inside the absolute value?

Tip: Always handle operations inside the absolute value before applying the absolute value itself.