I suggest the phrasal verb storm off , which encompasses the idea of leaving with anger.
I find the use of lope to be at odds with the need for anger in the motion, since a lope is "a long, easy stride; a leisurely canter"; ease and leisureliness are not compatible with anger.
As StoneyB says, I don't think you can get everything all into one word or even one phrasal verb; you will need additional description for the part where others are treated disrespectfully.
Other options for that portion could be elbowing people aside , barreling through the crowd , or even heedless of the people in his way .
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Stomp
I think you'll find 'stomp' perfect for use in this context.
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None of these words will fully serve your purpose.
Stride includes the notion of long steps .
Swagger and strut both include the notion of pride, but this is more an exaggerated regard for oneself than any direct disrespect for another.
None of these words includes the notion of anger.
I doubt that any one English verb will convey all these notions.
You will have to pick a verb which conveys the most important one, and add modifiers which convey the others.
For instance: He paced angrily forward; his humiliated followers could only scurry behind, unable to keep up with him.
He raged up and down in long strides, shouldering aside anyone who stood in his path.
He sneered and loped off in evident anger.
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One could plough through a crowd, angrily or not.
One might barge past some onlookers - to barge implies rudeness or indifference.
see also "he barged into the room, uninvited" I could also bull my way through the crowd
My ex-wife often stormed away in her anger at me and I would storm off in a fit of fury.
If you do so loudly, you might be said to thunder through or thunder past the startled onlookers.
A sense of *Charged angrily" would work too: In a fury, he charged through the crowd.
Hope it helps.
ell.stackexchange.com/users/5823/TedEwen
I don't know of a single word in my American dialect that quite captures it.
But He stormed off works pretty well if your person is leaving a room, or a group of people in a huff.
It's frequently used in that context.
"Stride" suggests a person walking quickly, but doesn't imply anger.
A silly woman leaving a situation in anger over something trivial, who wants everyone to see her leaving angry, can "flounce" away.
But dignified people don't flounce, and men don't either.
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I think that stalked is the perfect word….i.e. stalked across the room
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Is there a single word(verb) to describe the action "to walk angrily with long steps without giving respect other people"?  I found these three words which seem to be a close match for what I'm looking for: swagger, strut and stride. But I'm not sure which one of these I should use, or is there another other word that's better?
Word meaning "to walk angrily with long steps without giving respect other people"
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<word-request>
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"Stalked", "paced", "stormed off" or "stomped" convey the intended meaning. Stride, stalk and stomp work. You can also use phrasal verbs such as storm off.
Stride or stalk can work. Phrasal verbs such as storm off can work. Stomp works well.