I got this as a Maggie Smith nut - I've seen her on stage a number of times, and have been craving a film from her which matches the comic intensity which I've seen in the theatre.
Alas, this bizarre misfire doesn't give her a great deal to do. The other people have summed up the plot, so I'll just say that as a romantic comedy, this just doesn't cut the mustard.
The lighting (in the copy I saw, at least) looks more film noir than romcom - everything is dark and gloomy, reminiscent of Gordon Willis's cinematography for the office scenes in The Godfather.
Christopher Plummer has the kind of role John Barrymore used to play in his talkies - the cliché of the egotistical, verse-spouting actor. He does it very well, but his face is too dour to really charm as the hammy romantic lead. He does a good job with the young Italian, and is quiet funny there... but the dialogue and gags are lame.
And harking back to the old romcoms of the golden age, which often featured studio recreations of European capitals: alas, Budapest in the mid-80s looks dreadfully bleak - presumably the funding came from there, and part of the deal was to shoot it in the Hungarian capital. It looks terribly depressing and grey.
Maggie Smith looks lovely (when you can see her - that shadowy cinematography!) but even she can't weave the straw of the dialogue into gold (something she's usually able to do). California Suite, and bits of Murder by Death, seem to be the only film to really show here sophisticated comedienne stuff off on film.
Lily in Love, then, is one for total Maggie completists only (like me).
(By the way, the best 'lost' Maggie Smith film is definitely 'Love and Pain and the Whole Damn Thing' - seek it out, it's on DVD.)