Why did Liu Bei throw Lu Bu under the bus?

[Shampoo]

I expected the kind and generous Liu Bei would be the last person to deliver the killing blow when someone is begging for his life...

Sure Lu Bu did capture one of Liu Bei's provinces, but Liu Bei promised Lu Bu that province in the beginning so there were no hard feelings, then Lu Bu successfully stopped Liu Bei and some other guy from going to war against one another with his legendary archery skills, so Liu Bei should owe him a favor...

Not to mention, Lu Bu was a hero, he killed Dong Zhuo, freeing the Emperor and restoring the Han Dynasty, protected the Emperor and his lands while he was there. Isn't freeing the Emperor from Dong Zhuo the primary reason why these warlords took up arms to begin with? Even if some of them only cared about that on the surface, they still have to keep up their public image.

And here we have Lu Bu begging for his life, and Liu Bei told Cao Cao that he can not be trusted... Is this one of the rare times that we see Liu Bei's true nature? To betray a friend and hero of the Han Dynasty?

...

Also this might be a event in the game for Cao Cao, to either follow history and execute Lu Bu, or defy it, and recruit Lu Bu, so you guys might not need to wait for Dong Zhuo after all...

[Straybow]

Liu Bei betrays everybody, cause he's the hero.
Lu Bu had it coming though :)

[Haddon]

Lu Bu betrayed everyone he ever swore fealty to. He was a mad dog, and too dangerous to let live. Lu Bu was not a hero. He killed Dong Zhuo, but it was just one bad dude killing another bad dude. Stalin's Red Army pushing into Germany is what caused Hitler to kill himself, but that doesn't make Stalin a hero.

[Simonson [29th Ret.]]

Because Liu Bei is ultimately dishonorable and conniving.
Lu Bu saved him from Yuan Shu with the arrow shot, and when it came time for Liu Bei to return the favor, he sealed Lu Bu's death sentence.

[Nero]

Originally posted by No Limit Soldier:

Lu Bu saved him from Yuan Shu with the arrow shot, and when it came time for Liu Bei to return the favor, he sealed Lu Bu's death sentence.

Between that arrow shot and the death sentence Lu Bu attacked Liu Bei.

Besides did you not watch the TV series? Its one of the most memorable badass moments when Liu Bei tells Lu Bu how often he betrayed him, hence why he doesn't owe him anything.

[Jerroser]

Lu Bu had already betrayed him often enough that Liu Bei owed him very little by this point. Not to mention Lu Bu had already made quite a strong habit of betraying people for one reason or another.

Before joining Liu Bei and subsiquently turning on him. Lu Bu had joint both Yuan Shao and Shu, managing to annoy both of them by raiding their lands (while technically serving them).

[Eumerin]

Lu Bu betrayed Ding Yuan to join Dong Zhuo. Then he betrayed his foster father (which would have been a major cultural taboo), Dong Zhuo. Then he got chased out by Dong Zhuo's followers. He eventually received hospitality from Liu Bei, and promptly took over Liu Bei's city when Liu Bei was busy elsewhere. His later attack on Liu Bei was probably the last straw, as far as Liu Bei was concerned.

Also, it's not really depicted well in most media. But Lu Bu was apparently extremely arrogant - to the point where no one could stand him.

And finally, Cao Cao did give Lu Bu an opportunity to surrender before he besieged Xiapi. Lu Bu apparently took the offer seriously. Accepting it likely would have allowed him to survive But Chen Gong had deserted Cao Cao earlier, and knew that he'd be in big trouble if he fell back into Cao Cao's hands. So he talked Lu Bu out of surrendering.

[Darth Alpharius]

Liu Bei Only care's about his Brother's and the General's serving him, He also never cared for his own son tossing the baby to the ground.

[AlwaystheMage]

Originally posted by Darth Alpharius:

Liu Bei Only care's about his Brother's and the General's serving him, He also never cared for his own son tossing the baby to the ground.

That's a novel addition that just doesn't translated well in modern day. The idea behind that event is clearly not to turn Liu Bei into a baby hating monster but to show how much he cares for his generals.

On the original question

1) Liu Bei was kind but he was also ambitious and pragmatic. Even the saintly Liu Yu killed people, to be a successful warlord like Liu Bei was does require blood to be spilt. This is one of Liu Bei's less controversial killings

2) Clearly there was hard feelings. Liu Bei and Lu Bu never particularly got on by all accounts, Lu Bu tried and possibly a bit too hard that it creeped Liu Bei out. Add the taking Xu from under Liu Bei, that was never going to be forgiven. Lu Bu did one or two favours (returned family safely, the arrow thing but the latter was also in Lu Bu's self interest) but hardly gave Liu Bei a province to make up for it.

3) Lu Bu wasn't seen as a hero. Killing Dong Zhuo was considered a good thing and was a useful political tool (while ignoring his role in helping Dong Zhuo secure power) but there was likely some cynicism as to motive for that moment. Yuan Shu refused to take him in, Yuan Shao tried to murder him, Cao Cao and Liu Bei had no particularly reason to call Lu Bu a hero.

4) It was correct advice. Lu Bu probably, as Eumerin notes, would have survived if he had surrendered earlier (Chen Gong, how that treacherous, scapegoatting useless officers gets seen as a good guy...) when Cao Cao offered. That Lu Bu only did when captured left a decision to be made....

Lu Bu at this point was ageing had a bad record with loyalty and had an officer core+connections that meant he would have an army under him again if he rebelled. Lu Bu would still provide a good general but the risk/reward balance is very much towards risk of short term gain with dangerous revolt later.

[Simonson [29th Ret.]]

The incident of Liu Bei throwing his kid on the ground has become so well known in China that a proverb developed around it.

"Brothers are like limbs, wives and children are like clothing. Torn clothing can be repaired; how can broken limbs be mended?"

Kind of messed up.

[Darth Alpharius]

Originally posted by No Limit Soldier:

The incident of Liu Bei throwing his kid on the ground has become so well known in China that a proverb developed around it.

"Brothers are like limbs, wives and children are like clothing. Torn clothing can be repaired; how can broken limbs be mended?"

Kind of messed up.

'Torn clothing can be replaced' has more depth to it.