I have had some pretty unsuccessful experiences in talking to veg*ns about diet, so hopefully you can learn from my mistakes.
You may not want to start her off with The Vegetarian Myth. It's full of good information, but the tone is at times disparaging toward veg*ns. E.g., she refers to a vegan nutritionist as "some idiot" because she told a young couple that a vegan diet would be just great for their newborn. Granted, the baby died.... But apparently people don't like to be called idiots. It might turn her off at this point if it makes her feel attacked or insulted.
If she became veg*n for ethical reasons, you might want to show her some clips from Food, Inc. or interview clips with Joel Salatin from Polyface Farms.
Farms like Polyface produce soil creation of 0.5%-3% yearly, while every grain- or soy-producing monocultural agribusiness farm causes soil erosion.
Polyface uses no pesticides or chemical fertilizers, while grain farms generally use petroleum-based fertilizers.
Polyface treats their animals well, while Concentrated Animal Feeding Operations are full of abuses.
Polyface claims to be net carbon-negative because of carbon sequestration due to the way they collect and spread manure into the soil (rather than washing it away or collecting it as CAFOs do). Other "moderate" scientific sources disagree, due to the higher methane emissions of grass-fed cows (methane eventually converts to carbon in the atmosphere).
It is easy for me to believe that animals eating grains and pooping into concrete lagoons is harmful to the planet.
It's hard for me to believe that animals eating grass (as they are biologically meant to do) and pooping and farting onto the soil itself has a negative impact on the health of the planet via carbon emissions. So, I don't really care if Polyface is truly carbon-negative or not. It seems reasonable to conclude that the Polyface model is about as close to truly sustainable as you can get.
The bottom line is that if you are really concerned about environmental concerns, it makes no sense to be a grain-eating, soy-eating vegetarian. You cannot heal the soil without the animals grazing on the soil and fertilizing it.
Consumption of grains and soy directly supports the monocultural agribusiness farms that contribute to soil erosion, pesticide/herbicide/petrofertilizer use, loss of ecological diversity, etc. etc. etc.
If you are concerned about animal rights (humane treatment), then Polyface answers that objection decisively. Those are some very happy animals. Salatin jokes that they have a happy existence, but just one bad day.
(If you are squeamish about killing/eating animals, or if you have a principled objection to eating animals at all, then there's not much that anyone can say to convince you that you should eat animals.)
Combine all this with the health benefits of eating grain-free, soy-free Paleo, and it might be an easier sell.
I was at a Salatin lecture recently where he gleefully noted that ex-vegetarians are his best customers, because when they hear that pastured polycultural perennial agriculture is the fastest way to heal the soil, the vegetarians don't feel guilty about eating meat anymore, and they eat even more to make up for lost time. =)
As for practical tips on getting your sister started, take it slow and re-introduce various foods one at a time. Start by cutting out vegetable oils, soy, gluten. Add fish or whatever meat she tolerates/enjoys, coconut oil, maybe butter (if raw/grassfed/local, and if you consider butter close enough to Paleo). There's much more refining to do, but that's already a pretty good start!
If she is resistant to the idea of giving up vegetarian, she can still cut out soy and gluten, and eat soaked/sprouted lentils, beans, rice, etc. (At that point, though, my question to her would be, how is that any more environmentally friendly than local, grassfed meat?)