I think this depends on how you define liquidity, whether it's x * y or √ x * √ y.

In the article, I follow the definition of the whitepaper (in page 5, formula 6.3): L = √ x * √ y.

Thus, multiplying x and y both by 2 results in 2 * L = √ 2x * √ 2y = 2 * √ x * √ y.