Offer to make dinner, do the dishes, and anything else she does in the evening so she can afford to be tired.

You're going to get nailed with a bunch of "why do you want her to run? is this about you or about her?" questions, FYI

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maybe she's born with it, maybe it's chlorine
If you're injured and need some sympathy, PM me and I'm very happy to write back.
disclaimer: PhD not MD

As per above, why do you want her to run? Do you want the company? Is she not exercising at all and you are concerned for her health? What motivates her? Is she injured? One word of caution I have always found it is almost impossible to make someone change if they don't want to change.

Well, if by lab chems you mean cholesterol and triglycerides, I suggest you let her know you are concerned for her health and offer to exercise with her either early in the morning or after work. Also take a look at your diet, keep saturated fat <21 gms per day, cut all trans fats and go heavy on fruits, veggies and whole grains. Perhaps a class at a gym might be a good starting point. Also you could suggest that if she were to work out she would actually feel less tired. Start with baby steps, maybe just a walk/jog 3 times a week or something like that and increase slowly from there. Good luck.

if you nag her about it she WILL run--away from you!
suggest running together, unless you are super way faster..even if you slow down to her pace it will make her feel bad. I agree, help out with every thing else so she doesnt feel like it will be extra work besides the running...

take her shopping for some cute, comfortable, warm running clothes? only if she wants to run too though. otherwise, sorry. you'll have to search together to find an activity that she enjoys and will help her health. Classes sometimes are the best first-steps- like a yoga or weight lifting class, or, if you can afford it, a personal trainer. Quite possibly, the worst thing you can do is be her personal trainer...