How can Arrhenius bases also be Brønsted-Lowry bases? According to ChemGuide, 


  The Brønsted-Lowry theory doesn't go against the Arrhenius theory in any way - it just adds to it.


According to Study.com:


  All Arrhenius acids and bases are also Brønsted-Lowry acids and bases.


This makes sense for Arrhenius acids, such as hydrochloric acid. Hydrochloric acid produces hydrogen ions when dissolved in water. Additionally, it donates a proton to water.

However, sodium hydroxide is an Arrhenius base, since it produces hydroxide ions when dissolved in water. However, sodium hydroxide cannot accept a proton to form $\ce{HNaOH+}$. So, how can it be a Brønsted-Lowry base? Similar reasoning can be applied to other Arrhenius bases, such as potassium hydroxide.
Sure it can.  You're just incorrect about the products when $\ce{NaOH}$ accepts an $\ce{H+}$ in aqueous solution.  The result is $\ce{H2O(l) + Na+(aq)}$ instead of $\ce{HNaOH+(aq)}$.  That is, the $\ce{NaOH}$ doesn't stay together.

Now mind you, most people would point out to you that the $\ce{NaOH}$ doesn't stay together as soon as it's dissolved, meaning $\ce{NaOH(s) -&gt; Na+(aq) + OH-(aq)}$ happens right away, and then as soon as you have some $\ce{H+(aq)}$ around it reacts only with the $\ce{OH-(aq)}$ and the $\ce{Na+(aq)}$ doesn't get involved, probably isn't even anywhere near.  But this doesn't change the main point, which is that if you add $\ce{NaOH}$ to water, you have a solution that can react with $\ce{H+(aq)}$, which means you added a Brønsted-Lowry base.