The problem with "giving him Southampton" is that if it goes wrong then we have lost a six-pointer, wasted yet another plausibly winnable game under a new man, and lost more time to get a new man in...who will then have next to no time to use the window.
The whole point of replacing Frank after Brighton - at the latest - was to give us the best chance to save the season. If we're not going to pull the trigger now, then the upside of a new man is hugely diminished by the delay. At that point, we may as well stick with Lampard. The damage will already be done.