wrong data copied into new cell from macro

Try this:

Option Explicit

Sub Inspect()
Dim LValue  As String, LValue2  As String
Dim lngLastRow As Long, i As Long

lngLastRow = ActiveSheet.Range("A" & Rows.Count).End(xlUp).Row
  
For i = 1 To lngLastRow
    If InStr(Range("F" & i), "FORECLOSURE") Then
        If InStr(Range("J" & i), "DEFENDANT") Then
            If InStr(Range("G" & i), " V ESTATE OF ") <> 0 Then
                Range("N" & i) = Trim(Mid(Range("G" & i), InStr(Range("G" & i), " V ESTATE OF ") + 12, 100))
            ElseIf InStr(Range("G" & i), " V ") <> 0 Then
                Range("N" & i) = Trim(Mid(Range("G" & i), InStr(Range("G" & i), " V ") + 3, 100))
            ElseIf InStr(Range("G" & i), " VS ") <> 0 Then
                Range("N" & i) = Trim(Mid(Range("G" & i), InStr(Range("G" & i), " VS ") + 4, 100))
            End If
 
            If InStr(Range("K" & i), "  ") <> 0 Then
                Range("O" & i) = Range("K" & i)
            Else
                If InStr(Range("K" & i), "UNKNOWN SPOUSE") > 0 Then
                    Range("O" & i) = Trim(Replace(Left(Range("K" & i), Len(Range("K" & i)) - 1), "_", ""))
                Else
                    Range("O" & i) = Trim(Replace(Range("K" & i), "_", ""))
                End If
            End If
        End If
    End If
Next i
 
End Sub

The problem was you hadn't put in the UNKNOWN SPOUSE stuff anywhere, and you were only filling in your LValue variable when there were dblspaces. Since most of your variables were only being referenced one time, I took a bunch out and issued commands directly against the one-time calculations.

Also, based on your final instructions above, you had the wrong information going into N and O, backwards.