Lemon cucumbers have a slightly sweet aroma with a sour note, in addition to their prominent cucumber flavor. So, yes, they can be considered to have a sour component to their taste.
While the primary taste is that of a cucumber, and many describe it as fresh and fruity, the "lemon" in the name refers more to its round, yellow appearance than its flavor profile. It doesn't taste strongly of lemon. The sourness is a subtle characteristic that balances the sweetness and the cucumber flavor. It's not a dominant sour taste like a lemon.
Think of it this way: it's like a cucumber with a hint of sweetness and a touch of sourness. Therefore, you could describe it as having a sour note, but it is not overtly "sour" like a lemon.