LiHS

Certainly not a separate flight. The 10:30 departure from LHR is already better as it gives you 2h15min to connect in FRA, which is already a lot more comfortable than 1h15min. I see this is the longest connection lufthansa.com will offer, however you can force a longer connection using either Google Flights or ITA Matrix with Powertools to select flights and feed them to lufthansa.com. There are hourly LH departures starting at 6:30, so you can pick the connection time which best balances your risk appetite and willingness to schlep to Heathrow at an early hour.
Note you can combine LHR-FRA-TIV (LH, Sundays only) on the outbound with either TIV-MUC-LHR (LH, Saturdays only) or TGD-VIE-LHR (OS, any day of the week) on the inbound if you want more date/time flexibility. Both MUC and VIE are much quicker/easier to connect in on the way back. They are also earlier in the day, so there are several later flights to LHR they can rebook you on in case of a misconnect. Thus you can happily book the shortest connection that pops up and not worry about getting home the same day, whereas there are only one or two LH flights leaving FRA after the TIV flight arrives there so a misconnect would mean overnighting in FRA courtesy of LH.

Beverages. Specifically ones with ethanol. If that's your thing of course.