Some thoughts around the standard Atkins portion suggestion of 113g / 4 ozs of meat per meal:
You're trying to achieve an overall balance of fat and protein, with negligible carbs.
If you choose lean protein sources, rather than ones that fit the above objective, then in my experience it gets more difficult.
115g of 20% fat beef mince for example is a good fit, as are some of the
oily fish, hard cheese and eggs. They come with the right balance of
fats and protein built in.
If you choose 115g of a lean protein like turkey breast you'll get 33g
of protein and very little fat, If you then add 30g of fat to compensate
you end up with a lot more intake - 60% more - than if you chose 115g
of 20% fat beef mince.
If you use lean protein sources aim for less than the standard portion to compensate.