Create a constructor for the FrmGoogleMap class which takes two parameters:
Public Class FrmGoogleMap
Private fParallelLines1 As List(Of PointLatLng)
Private fParallelLines2 As List(Of PointLatLng)
Public Sub New(ByVal pl1 As List(Of PointLatLng), ByVal pl2 As List(Of PointLatLng))
fParallelLines1 = pl1
fParallelLines2 = pl2
End Sub
Then just pass them when you create the instance:
Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
Dim f As New FrmGoogleMap(fParallelLines1, fParallelLines2)
f.Show
f.DrawFence()
End Sub