Is there an actual way of figuring out which lender will have the best
interest rate, or are they all going to be essentially similar enough
to where it doesn't matter that much? In that case, I would be best
off choosing the lender who is easiest to work with and has the most
competitive closing costs, or some other factor that is important to
The short answer is: You likely have to inquire with multiple lenders to find out. The variance in rate/closing costs can be significant.
What I've done recently is get quotes from several prospective lenders, lock in the best rate/closing cost combination, then shop that offer around with the other lenders (I was getting daily updates for a while). Nothing about locking my rate obligated me to proceed with that lender.
The only reason I took a more aggressive approach with shopping around and hunting daily rate differences is that I have multiple loans to refinance and wanted to see if there was much variance/flexibility. Based on my recent experience, I'd suggest comparing rates just between your original lender and a few other reputable lenders and calling it a day. The variances that I've seen from day to day have not been terribly significant other than the recent addition of the adverse market fee which was a binary event for each lender (though they each seem to have added the fee at different times). Shopping the best rates around to other lenders was not very fruitful either, I'd only do that if you have a strong preference on which lender you want to use.
If you do want to wait and see if rates drop significantly in the short term, lock in a good rate first with one lender and check back with other lenders a couple times during your lock period (just mind the deadlines). Some lenders will mitigate risk of rates dropping after you lock in by increasing their lender credit if rates drop, so that's worth asking about as well.
Another situation where it could be worth checking back over a couple days before locking in a rate is if you don't get an appraisal waiver on your initial quote. To me that was just as much about the several hundred dollar savings as it was the hassle to myself/tenants.
Make sure you get some variety in your prospective lenders (credit unions, traditional banks, online mortgage lenders, private brokers), historically I've used a local credit union but for my refinance spree Quicken loans has happened to have the best rates in most scenarios, that doesn't mean they'll have the best rates for you.