Lemon dill sauce broke [duplicate]

There is no way to be certain, but I would blame the margarine.

Margarine is not pure fat like an oil, nor a simple fat-water emulsion like butter. It is a rather unstable emulsion, and it uses all kinds of industrial tricks to achieve a smooth, soft, spreadable consistency. It is not just emulsified, it generally contains all kinds of gums too. This is especially pronounced in reduced-fat margarine products.

You shouldn't heat margarine, as you never know how it will behave under heat. It is a bit less of a problem in baking, if you are willing to accept large differences in texture; but as you noticed, it can be very problematic in foods where the correct texture has low tolerance.

If you want to reduce your butter consumption but still make roux-based sauces, use any liquid oil. You can use a cheap vegetable oil for strongly flavored sauces, or an oil with its own taste for milder sauces which can profit from more flavor.

The ratio of fat to starch in a roux is not very tolerant to fat reduction. You should always use at least 1:1 fat to flour. A little deviation (such as using 1:1 butter to flour, which makes it 0.83 fat to 1 part flour) will still work, although it is recommended to up the fat a bit when using butter. But you cannot reduce the fat in a roux-based sauce by choosing a fat-reduced product (assuming you could find a gum-free one) instead of fat and keeping the overall ratio the same. So, if you are looking to reduce your total fat consumption during Lenten and the use of 1:1 oil to flour ratio is not acceptable to you, you will have to do it by some other means.