I was lifting while training for a marathon (26.2 miles). I don't do long distance running now because I find the endurance training counterproductive to my goals of adding muscle and lean body mass. However, I adjusted my training schedule at that time to do my long run on one day, have a full day of recovery, then I did my leg day with weights the next day.
If I did my longest run after weights it negatively impacted performance, if I did them too close together I was very prone to injury.
I had to look up what exactly a duathalon is - sounds like a fairly short run, bike, then another short run. I think this could be compatible with your weight training with legs, but like my long distance training I'd probably try to schedule the hardest running days far enough away from one day of leg training with weights, stretch a lot, maybe do some low impact cardio on some days (like elliptical), and most importantly listen to your body - fine tune your training as needed.
Good luck with your training!
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