No immigration needed as you're arriving from a UK destination. If you have no checked baggage then you would need, at worst, to exit T3, walk for less than 5 minutes over to T1, then upstairs to Departures and through security. 95 minutes is more than enough for that, especially if you've checked in online with LH and printed your boarding pass. Before the recent refurbishment of T1, you could even walk from your T3 gate to your T1 gate without eciting the secure area (just by following the Flight Connections signs). This may still be possible.

With checked baggage, Air Southwest should be able (but may not want) to check your baggage through onto the LH flight. That is the ideal solution and makes 95 minutes more than enough time. Agai, you might be able to simply walk to your LH departure gate without even a security check.

If Air Southwest do not want to through-check your luggage onto Lufthansa, then you will need to reclaim bags. This is the biggest delay factor and it may take you 20-30 minutes in total from touchdown to getting your bag. That still allows 20 minutes to get upstairs to T1 check-in, but clearly isn't as comfortable.