Answer:
If the current price of $\$30$ is after a $50\%$ reduction, then the Lux basketball shoes must have been $30 \times 2 = \$60$ before. That $\$60$ price was after a $25\%$ reduction. When $25\%$ of the price is removed, the remaining portion is $75\%$, or $3/4$ of the price, which means the original price must have been $\$60 \times 4/3 = \boxed{\$80}$.