I see "lust" as the equivalent of "covet". In other words, it requires a mens rea to formulate a plan to take a married woman away from her husband or to induce a married woman to violate her marriage vows.
When I tell someone that I like his new Ferrari, I'm not coveting his property. If I begin to formulate a plan to deprive him of it so that I can have it, now I'm coveting.
If I note the beauty and sex appeal of my neighbour's wife, but I have no intention, plan or thought to contrive a situation where she will violate her marriage vows, I have neither coveted nor lusted.
King David's thoughts and plans regarding Bathsheba are (in my opinion) the archetypical example of lust or coveting. He saw, he thought, he planned, he intended to execute the plan. This is the same sin as executing.
In my opinion, Matthew 5:27-30 has been misunderstood, especially as regards young unmarried men (and women) and the natural thoughts they have towards attractive members of the opposite sex. Too many young unmarried men, full of their God-given hormones, are driven to needless guilt and anxiety over their attraction toward the young women they encounter. Much guilt and anxiety results from fruitless attempts to purge one's mind of all prurient interest, even when no attempt is made to act on such impulses and when the young man's actions are entirely respectful and in keeping with Christian standards.