Investment Property HELOC question - located in Memphis Tennessee
It would be very difficult but would not be impossible. Most bank and lenders online have a minimum loan amount size, your best bet is to try to find a local retail bank.

Do lenders have to lock in your rate before appraisal?
No... you can decide to float your rate all the way to docs being cleared. Once your loan is clear and approved from underwriting you can decide to lock and doc your loan at anytime. Please keep in mind that your appraisal is usually only good for 90 days. Give me @ New American Funding Direct @ 1-800-450-2010 x...

Can we get a HARP 2.0 loan from a different lender when we currently have PMI?
You can refinance through any lender that offers the HARP 2 program.

What's a float down option?
If you lock your loan at an interest rate of say, 4.25%, and rates drop to 4.0%, you can take advantage of the lower rate, during the original term of your lock.