Oftentimes, we equate legato playing with being lyrical or lyrical playing as being legato. It brings up two interesting questions: What is legato? and What is lyrical? Looking at them separately, we can see their differences and their relationship.
Legato is a form of articulation which connects one note to another note as smoothly as possible. Many times I hear trombonists and their legato sounds like a very smooth tenuto. My legato can sound to glissy for some. My feeling is that the music should dictate what kind is used. There is a spectrum of legato just like there is of anything else. The more tenuto style can work very well in early music and playing with other valve instruments like in a brass quintet. The other more liquid form of legato can work beautifully in many solo things of a romantic nature as well as in many big band or jazz type solos.
But what is lyrical? When we see that a song has lyrics in it, we don't think, "Who wrote the legato to this piece?" We see words. Lyrics are words and we associate words in music with vocal productions and singing. Lyrical poetry. Songs can be poems that are sung. Lyrical speaks of a language of emotional content and expression. So what is the language of emotional content in music? It would be inaccurate to say it is legato. Legato is a technical term to describe a form of articulation. It says nothing of emotional content. But could it provide a color and sonic texture that could be supportive to certain types of lyrical natures? Sure.
Now, does something need to be legato to be lyrical? When we think of many songs it is easy to find a number of them sung in a legato manner. But, many are very articulated with a variety of dictions and punctuations that would be far away from what we generally consider to be legato. Think of all the non-legato lyrical aspects of opera to rock and roll and beyond.
The next time you play something that is not marked legato, ask yourself about what you are doing to provide lyrical content to it or if you think the piece calls for some. Making note values longer does not necessarily provide the element or emotional content to make something sound more lyrical. Finding the inner 'poem' of the piece (from your perspective ) is one way to have the music's unwritten but not unfelt lyrics come alive.