Using Select fails sometimes for no apparent or reasonable reason.  In your
case, you can do without it

lngLastDataRow = Cells(Rows.Count, 1).End(xlUp).Row

all in one go, no selection.

Are you trying to select A65000 on one sheet using a macro from another
sheet?  That's not permitted.

I forgot to mention that if you put that code in a module, you can use
it from any sheet.

If this code is behind a worksheet, then that unqualified range refers to the
worksheet holding the code--not any other sheet that you may have selected.

Just to summarize because all answers have not been consistent:

Assuming that as others have surmised, the code is in a sheet module for a
sheet that is not the active sheet.  For discussion purposes assume a
Commandbutton1 on Sheet1 has been clicked.

Private Sub CommandButton1_Click()
Dim lngLastDataRow as Long
With Worksheets("Sheet2")
    .Activate
    .Range("A65000").Select
     Selection.End(xlUp).Select
     lngLastDataRow = ActiveCell.Row
 End with
 ' do something with the results
End sub

As Dave said, an unqualified Range reference implicitely refers to the sheet
containing the code.  So the above qualifies the reference.

But better is as Juan suggested

Private Sub CommandButton1_Click()
Dim lngLastDataRow as Long
With Worksheets("Sheet2")
    lngLastDataRow =  _
      .Cells(rows.count,1).End(xlup).Row
 End with
 ' do something with the results
End sub

Of course either of these constructs would have to be repeated in the "do
something with the results" part of your code or you will encounter the same
problem.

Hello world:

Yay! It works!

Many thanks to all of you for answering so quickly and correctly.
As many of you surmised, I was trying to run one sheet's code on another
sheet.
When I moved the code to my code module, and called it from there, it worked
fine.

Whew!  That was driving me nuts (and I don't have far to go).

Thanks again.

Alan