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A Brønsted-Lowry acid is defined as a species that donates a proton (H+) in a reaction, while a Brønsted-Lowry base is a species that accepts a proton. On the other hand, a Lewis acid is a species that can accept an electron pair, while a Lewis base is a species that donates an electron pair.

Now that we understand the definitions of Brønsted-Lowry and Lewis acids, we can compare their chemical behaviors. When a Brønsted-Lowry acid donates a proton, it leaves behind its conjugate base. This conjugate base often holds a negative charge due to the loss of the positively charged proton. A Lewis acid is a species that can accept an electron pair, meaning it can form a new bond with a Lewis base which donates its electron pair. Since the Brønsted-Lowry conjugate base is left with a negative charge, it has available electron pairs, making it capable of behaving as a Lewis base, thus allowing the original Brønsted-Lowry acid to act as a Lewis acid in the process of donating its proton.

It's important to look for any potential exceptions where a Brønsted-Lowry acid may not necessarily behave as a Lewis acid. When analyzing the properties of the conjugate base, we see that there is an important condition: if the conjugate base is a strong Lewis base, the original Brønsted-Lowry acid will likely not behave as a Lewis acid, as there is a competition between the electron donation of the conjugate base and the Lewis acid behavior of the molecule. An example of this is hydrochloric acid (HCl). HCl is a strong Brønsted-Lowry acid, which donates a proton to form chloride ions (Cl-). Chloride ions are strong Lewis bases, which readily donate electron pairs, making it difficult for HCl to behave as a Lewis acid.

Although there are cases where Brønsted-Lowry acids can act as Lewis acids, it cannot be concluded that all Brønsted-Lowry acids are also Lewis acids. This is due to the potential competition between the electron donation of the conjugate base and the Lewis acid behavior of the molecule. Therefore, not all Brønsted-Lowry acids are Lewis acids, as there may be exceptions in certain cases, such as strong acids with strong conjugate bases like HCl.