I am a US student planning to spend 8 weeks working in a university research lab in London during May and June 2017. I am not traveling through any study-abroad program. The primary investigator just agreed to let me spend 8 weeks gaining research experience. It is unpaid. I am confused as to whether I need a Tier 5 visa because I will be doing "unpaid work" or whether I do not because the gov.uk website says that people participating in academic research do not need a visa?? I don't think I qualify for a student visa because I am not enrolling in the university .
You want to spend some time (8 weeks) in a UK research lab, but not as part of any formal programme, to gain some research experience. You will not be paid.
What visa do I need?
You will need either a Tier 5 or Tier 2 visa. The activity you described is not covered in the permitted activities for the Standard Visitor Visa. The fact that you will not be paid is irrelevant and may even get the research lab in trouble for offering unpaid employment to an individual who is not an EU national. It's a hefty fine for them to take you on without having permission from the government to do so. So be careful not to let them get caught!
Having said all of that, our sister site, Expats, will be able to answer further questions about specifically what kind of T2 or T5 you need.
The primary investigator just agreed to let me spend 8 weeks gaining research experience
Print out this answer and show it to the PI :)