Sundrome,
I worked as a scientist in biomedical research for well over ten years prior to attending veterinary school (I specifically returned to vet school to specialize in LAM). I didn't have specific pre-vet internships in LAM per se, but did interact with many lab animal veterinarians throughout the course of my career. I met the first lab animal vet with whom I had significant interaction in graduate school. He troubleshot some significant problems that were happening with my project, and has been a true mentor ever since. In every environment that I've worked, both industrial and academic, I have made a point of getting to know the lab animal resources staff- veterinarians, technicians, and administrators. This is the way I gained my LAM experience, alongside conducting the actual science itself.
Are you still in undergrad? Interested in lab animal medicine, and just wanting to see what the field is about? Are you planning on applying to vet school in the next year? During your internship, I recommend that you pay attention to how LAR staff support the science that's being conducted at the institution you're at. Just like in private practice, lab animal vets need good communication skills to effectively interface with principal investigators, academic administrators, regulatory officials, and animal care staff (among others). Ask your supervisors to tell you, in all honesty, what they love and dislike about the career. LAM is broad- there are opportunities for specialization, even within LAM (some folks do strictly regulatory, some are mostly clinical, most are a combo of regulatory/clinical/admin). Ask about the differences in the research (and the role of a lab animal vet) in academia, industry, and government.
When it comes to the clinical work itself, pay attention to how LAM is actually conducted. This is a population based field, and is less focused on individual animals. In many ways, it is very similar to food animal medicine. Ask about how disease outbreaks are controlled, and how these can potentially affect the research (and livelihoods of the scientific staff that conduct the work) occurring at the facility.
Mainly, you want to get an idea of what a lab animal vet does on a day to day basis. It's a good opportunity to get your feet wet, and to interact with some interesting people in a novel environment. Take advantage of that, and good luck!