To find out how long of a piece Louisa wants, we need to calculate \( \frac{1}{3} \) of \( \frac{4}{5} \) yards. We can do this by multiplying the two fractions:
\[ \frac{1}{3} \times \frac{4}{5} = \frac{1 \times 4}{3 \times 5} = \frac{4}{15} \]
Therefore, Louisa should ask the sales attendant to cut \( \frac{4}{15} \) yards of fabric for her cat's t-shirt.