I think Louisa is insecure and Martin is clueless. That seems to be a constant theme between them - in and out of bed
But what strikes me about those two "engagement" episodes is the lack of physical affection between the two. I don't expect huge PDAs from Martin, but he seems surprised that Louisa expected to spend the night after the nutritious dinner. It is once again Louisa taking the initiative for any physical intimacy. He says he is pleased -- but if she hadn't brought it up, would he have asked her to stay? For that matter, why did they not just move in together once they were engaged?
It's not a question of sex, but rather the idea that, as an engaged couple, they would have wanted to spend their time together.
Which leads me to the conclusion, which I think we've often discussed, that Martin is, in Series 3, more in love with the "idea" of Louisa than with the actual woman. He doesn't know her that well. And it leads me to think that some of his actions, like suggesting the nasal strips, pointing out her use of salt on potatoes as unhealthy, were unconscious attempts to end the engagement before they reached the wedding day.
I don't think it was necessary or appropriate for them to move in together. Both are rather traditional that way, and I think living together after they were married seemed to fit DM best, and maybe LG, too, being the head teacher at school. After all, it may indeed be that DM didn't feel comfortable having sex without a clear sense of deep commitment between them. He had intimacy issues, absolutely, but it also seemed that he wanted real commitment before having sex, which is old fashioned, indeed, but also kind of sweet.
Well, in S4 we learn that they did indeed have sex more than the once we know for sure, and the one we imagine happens, the after the nutritional dinner sex. It seems from LG explaining to EM when she and DM had sex, it was more than just twice. So, what we see on screen is not wholly what happened between them behind scenes. And, DM does do the leaning forward of the kiss on the patio scene, and is obviously very sorry (sorry, sorry, sorry) his phone interrupted them. I think we are led to believe he would have initiated that bit of closeness if his duties had not stopped them. That sort of bonding no doubt happened more than that, and we were given a brief glimpse of some of their off screen closeness.
And, even though I think they spent close time together, we do see that LG and DM are going to have to adapt as a couple to him being on call 24/7 as the doc to PW and surroundings. We see that theme from the get go at the beginning of their relationship and all throughout all of the series. DM is as committed to his duty of care as he is to being with LG.