Store the assc. label in the tag property and you can cast it back when you click on the button. The sender object is the button that is currently clicked.
Dim FILE_NAME As String = "D:\1.txt"
Private Sub Form1_Load(sender As Object, e As EventArgs) Handles MyBase.Load
Dim i As Integer = 1
For Each line As String In System.IO.File.ReadAllLines(FILE_NAME)
Dim NextLabel As New Label
Dim Nextbtn As New Button
Nextbtn.Tag = NextLabel
NextLabel.Text = line
Nextbtn.Text = "Copy"
NextLabel.Height = 22
Nextbtn.Width = 55
Nextbtn.Height = 22
NextLabel.BackColor = Color.Yellow
TabPage2.Controls.Add(NextLabel)
TabPage2.Controls.Add(Nextbtn)
NextLabel.Location = New Point(10, 10 * i + ((i - 1) * NextLabel.Height))
Nextbtn.Location = New Point(120, 10 * i + ((i - 1) * Nextbtn.Height))
AddHandler Nextbtn.Click, AddressOf Me.Nextbtn_Click
i += 1
Next
End Sub
Private Sub Nextbtn_Click(sender As Object, e As EventArgs)
Dim s As String = DirectCast(DirectCast(sender, Button).Tag, Label).Text
End Sub