Can I add $1500 to the cost basis of my second home without receipt for the parking lot repair in front of the garage?.

It would be better if you had the receipt, a cancelled check, or a bank statement showing the expense added to the basis of the second home.  You can go ahead and include it as part of the cost basis.  It is unlikely that you would be expected to justify the amounts that you enter as the cost basis for the second home.  

Just keep in mind that if your return were being audited for any reason, everything being reported is subject to further scrutiny.  If you did not have the documentation, then the numbers would be adjusted at that time.

That depends on what the bank statement shows.  In tax situations where a taxpayer is required to substantiate a deduction, expense, or as in your situation, the adjusted basis of a home, the specificity of a document is what matters most.  If a document, such as a bank statement, shows $1,500 was withdrawn and nothing else, it might fail to substantiate the adjusted cost basis because the bank statement does not show to what the $1,500 relates.  However, and to follow-up on the comments from @AnnetteB6, go ahead and include the expense in the cost basis of your home.  If the home sale should face additional scrutiny, you might have to make adjustments to the cost basis. 

@tuanngnttax