The Opera North production at Sadler's Wells in London circa 2002 made the sexual nature of their relationship quite clear.
Perhaps after two decades my mind is embellishing the memory, but during 'A Little Priest', Mrs Lovett was slightly bent over her pie table, and Sweeney stood behind her and grabbed her hips; she bent forward a little more. There was a little playful swaying from behind and pleasurable, playful moans as the song progressed. There was no outright thrusting nor was it comedic, but it was definitely very sensual. I think the pause after 'With or without his privates?' was used as a brief opportunity for both to compose themselves before continuing.
However, what I do remember very clearly - as a Sondheim-obsessed 20 year-old who'd been regularly listening to Sweeney Todd for years - is being in that audience and thinking: 'Of course! How did I not realise until now that they're fuc*ing?!'