Honestly, the fact that you ask the question makes it pretty likely that the gun is capable of better accuracy than you are, at this point. (This is not meant as an insult, BTW, I've been shooting for years and used to compete in amateur action pistol competitions frequently...and my LC9s is probably capable of better accuracy than I can manage with a small pistol and my aging eyes.)
So, to answer your question, by all means you should shoot targets as frequently as possible with the LC9s, especially if you are planning on carrying it or keeping it in the night stand. You won't be competitive against more experienced shooters and guns designed for bullseye shooting, but no range time is wasted time, in my opinion. Don't expect to out shoot guys that are likely using guns with higher inherent accuracy and a longer sight radius - just concentrate on improving your personal best with the gun you have.
My LC9s is pretty new, but it points quite naturally and is all I'd ask for in a CC weapon (well, except for the sights, those "white" dots are more like light gray on dark gray to these aforementioned aging eyes, so I have a TFO set on order). Fast double tap exercises at 10' are about as good as from my full-size .40's, but I'm barely using the sights for that. At 25' double taps open out quite a bit but are still in the 8 ring (most in the 9) of a typical silhouette target. I might get tighter groups at 25' after the TFO sights get here, we'll see.
By contrast, I find it pretty easy to keep all my double taps in the 9 at 25' with my Glock 22C with TFO sights.
John