Despite the title and the poster it's not super romantic, traditionally. Less cute romcom, more chaotic romcom. Generally speaking, it gets better as it goes, especially once you get acquainted with the characters. The main character, in particular, takes a while to warm up to, even now that I've finished the season. However, he does feel like a genuinely relatable person, or like a real person, and that's a good thing. It's not as if he was written to be anything other than himself. The tension between the two main characters felt awkward, yet it seemed realistic and added to the authenticity of the show.
The story isn't overly complex or convoluted. You can sense a twist coming later on, but it's not grandiose or mind-blowing, but it maintains a believable quality. The humor isn't riotous, but it does have a simple genuine feel. British humor. Music is occasionally used to enhance this, especially in the first episode. Towards the end, it's less about humor and more about the affair, the show's vibe keeps a balanced tone without going overboard. The series doesn't try to do too much in general.
If you're not accustomed to watching British sitcoms like this, I'd recommend starting with something like "Catastrophe" first. It's a better introduction and helps you get accustomed to the humor and style. The title "The Lovers" can be a bit misleading, so if the first episode doesn't resonate with you, it's probably best to skip the rest. However, if you do like it, then by all means, continue watching. I think the first episode's a good test.