Lemon dill sauce broke When making a lemon dill sauce will limited ingredients due to Lenten restrictions, we found the sauce broke after simmering.  The sauce was vegetable stock with lemon juice then thickened with a roux of margarine and flour.  All was well for 10 minutes at a low simmer when suddenly it broke.  Did the lemon break the gluten?  Did the simmering cause the breakage? Was the margarine the cause?
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.