Be prepared that if you are bound and determined to buy in the current market you could very well end up with the house appraising for less than you are offering, and would have to come up with the difference CASH (if this is a surprise, PM me for a full explanation). 

When you close, there's no bank, no points, no appraisal - you just close with your own cash. 

My lender doesn’t seem sure about my question if my signed lease agreement supersedes the rental appraisal.

The way to get a house right now is to offer all-cash and waive appraisal.

In inflated markets (a condition you can gauge by the increasing gap between asking/offer prices and the prices at which homes APPRAISE) profitability tends to shift away from buy-and-holding turn-key properties to favoring the rehab space of investing, flips and BRRRR. 

Have you seen appraiser give tile more value ?

I owe 141 on the house at this point so at those numbers a heloc isn’t worth getting, I do feel as though the appraisal is low.

During my first investment, I was able to purchase under market value 🙌 , and with some rehab it now appraises at 20-25% over the initial purchase+rehab cost!

Now, just feet from the finish line our appraiser is not getting info back to us in time for our closing...its gonna be tight.

Now I owe $137,000 and the appraisal appraised it for $240,000.