What have the L-systems (Lindenmayer systems) been actually used for in biology?
Are these models important? Still taught?


Yes!! These models are extremely important, however, the application of L-systems most definitely isn't confined to just the scope of Biology. I myself first came across L-systems when taking Calculus in university, and then later in several Computer Science courses (I study Bioinformatics). 

What's (probably) most significant to mention about L-systems is that they produce fractals, which is acheived by defining a substitution system and utilizing recursion.

Fractal mathematics can be used to describe extremely complex phenomena, starting with just a few simple rules and initial conditions (which is why it's so powerful/attractive to study). Also, fractals have the nickname of, "God's Thumbprint", or, "The Fingerprint of God", just from where they're found so prevalently in nature. To name a few, fractals can "easily" model:


Coastlines
Blood vessels
Brain structure (neuronal connectivity)
Plant foliage 
Lightning bolts
Diamonds
Snowflakes



  I tried to find biological research that has actually used this system but I could not find any.


As you can see, some of these examples are biologically related, however, the use of L-Systems have been broadened to many other fields of science, such as mathematics (coding theory) and theoretical computer science. 

Unfortunately, very rarely do biologists have the mathematical or algorithmic backgrounds to work with L-systems, since L-systems are more related to mathematics, algorithms and logic, than they are with (practiced) biology.