Ops, non avevo letto bene e avevo capito che era una textbox o qualcosa del genere (anche perché ASP.NET viene trattato in un altro sottoforum).
Allora:
codice:
        Dim cella As System.Web.UI.WebControls.TableCell
        Dim riga As New System.Web.UI.WebControls.TableRow
        Dim leggi As New IO.StringReader(lettura.DownloadString("ftp://ftp.uploadgenius.com/uploadgenius.com/Accounts/Real/SHJWYWG178/" & Label2.Text & "/lstfilelog.txt"))
        Dim memoryStream As New MemoryStream()
        Dim streamWriter As New StreamWriter(memoryStream)
        streamWriter.Write(leggi.ReadToEnd)
        streamWriter.Flush()
        memoryStream.Position = 0
        Dim streamreader As New StreamReader(memoryStream)
        Do Until streamreader.EndOfStream
            cella = New System.Web.UI.WebControls.TableCell()
            cella.Text = streamreader.ReadLine
            riga.Cells.Add(cella)
            Table1.Rows.Add(riga)
        Loop