This is one of those questions that depends on the level of detail you want to attain. The first, most useless answer, is that it depends on your goal. However, if you are lifting, in almost all cases it is better to run after you lift. Running does tire out your muscles per se -- your triceps, shoulders, and pectorals do not do a lot of work running but benching after running will cause a drop in performance compared against a 'fresh' bench press -- it's more a question of metabolic conditioning and glycogen supply. The general principle (derived from Selye's theory of stress) is that your body adapts to the stress applied to it, and you can only apply so much stress at one time so you're best off lifting first.
With that said, if you are training as a runner you are best off training for your sport first. There are many reasons you might want to lift afterwards, but it would be a specialized kind of lifting -- for joint health, for instance. It would incorporate an exercise selection, intensity (weight), set and rep scheme, and rest interval all specifically geared towards that one goal. The more advanced you are, the more stress you need to apply to spur adaptation, the more zany your training protocol becomes.
One thing you DO want to do is properly warm up before lifting. Five to ten minutes of low intensity, low impact, steady state cardiovascular activity will increase the temperature of your tissue and increase the blood supply. This makes muscles better at all the things they do as well as increasing flexibility (and decreasing injury in turn). You also do warm-up sets before lifting with your working weight for that and some other reasons.
But again, it all depends on the level of detail. In general, if you plan to lift and run just for basic health you're best lifting first and running afterwards.