Are there major obstacles to completing a thesis Masters program if I'm not funded/working in a lab?
It strongly depends on your school, your department and your topic. Ask your advisor and/or PhD student what is the policy of the department.

There are theses where student work for a lab or factory and the thesis is part of this work (optimisation tasks, design of custom experimental apparatus), there are also, mostly theoretical, theses that can be succesfully defended and continued in PhD without strong bond with the department.

There are also topics, ususaly narrow-focused, where student is not skilled enough to work for the lab. Or there may be legal issues.