So the lighting is what causes my photos to appear flat?
Yep

you're learning
Am I safe to assume better lighting would also help with getting a cripser, sharper image?
Never
ASS U ME 
but define "better". Definitely
different would be helpful as in get the light OFF-CAMERA
Just seems like others are able to achieve almost 3-dimensional photos, whereas mine just look BLAH.
Look up
Inverse Square Law & think about light sources. You don't need to invest in a HARD CORE gear, yet, to give the 3D view to your images but at least one flash unit with capabilities to have it off-camera would be a good start.
You UNDERexpose the scene and light up your subjects thus have them
pop-up in a sense from the scene. Also direction of the light also very important. There will be times when you just want to have this flat looking imageIf or have time just for one shot - thus take it and go; however, if opportunity permits, why not make the image
better. Unfortunatly there are people out there (pros and amateurs) who do not know fundamentals of light, how it works and what to do with it. Yet charge tremendous amount of $ and put out crappy product. Stay in photography long enough and you'll see this time and time again.
If you don't want to believe me and take my word for it, look at any PRO-OUTDOOR model shoot. TRUCKS pull up with lighting gear, permits have to be acquired to set those up, its a huge production. Look at Hollywood films, those are gigantic 18wheelers with continues lights, huge softboxes, all meant to
imitate natural light and yet control its direction, intensity, etc etc.
Natural (outdoor) light, as I said, is pretty boring (unless we're speaking of this
Golden Hour). Learn to control it and it'll improve your work tremendously.
PM if you want to talk specifics.