Apart from a couple of pantyshots and unintended touches of her big... badonkers, I wouldn't call their fake relationship "lewd". But his daydreamer side is starting to show and I'm sure that will be the major source of the actually lewd visuals in this going forward.
Oh, there it is. There's a time limit. They have to somehow convince her parents by the time a month is up. Maybe get her to genuinely fall in love with him by then. It would be great if this actually leaves the "fake relationship" plot point behind soon, have them date for real early on, and the majority of the series would be about them dating for real and managing the challenges that come with it. That would at least make this stand out a bit more from many male-oriented romcoms that always end when the main pair starts dating.
I've never really liked arranged marriage subplots though, so this could be a little painful for me when the time to face that conflict comes, and they're not ready to face it.