Not only Bhima, Krishna also had insisted *Yudhishtira* to lie about Ashwatthama before Drona's death, as it was evident that Drona (aware of his son Ashwatthama's capabilities) may not trust Bhima alone and may approach Yudhishthira to seek the truth.

My question ["Meaning of Krishna's advice to Yudhisthira before Drona Vadh"](https://hinduism.stackexchange.com/questions/7356/meaning-of-krishnas-advice-to-yudhisthira-before-drona-vadh) is on the same event but different aspect. [Its source](http://www.sacred-texts.com/hin/m07/m07187.htm) actually answers your question:

> Govinda, knowing that Drona, that foremost of warriors, was capable of
> sweeping all the Pandavas off the face of the earth, became much
> distressed. Addressing Yudhishthira he said, 'If Drona fighteth,
> filled with rage, for even half-a-day, I tell thee truly, thy army
> will then be annihilated. Save us, then, from Drona. under such
> circumstances, falsehood is better than truth. By telling an untruth
> for saving a life, one is not touched by sin. **There is no sin in
> untruth spoken unto women, or in marriages, or for saving king, or for
> rescuing a Brahmana.** <sub>1</sub>
> 
> <sub>1: This verse is omitted in the Bombay text. There can be no
> doubt, however, about its genuineness.</sub>

Somewhere Krishna suggested Arjuna that to establish *Dharma*, if little *Adharma* is required then let it be. For example the fight of [Bhurishrava vs Satyaki](http://www.ishafoundation.org/blog/sadhguru/masters-words/krishna-in-mahabharata/) during Jayadratha Parva:

> <sub>Krishna told Arjuna, “Burishwara is going to kill Satyaki. You must
> get Burishwara first before he kills Satyaki.” Arjuna said, “How can I
> do that? Burishwara is fighting with Satyaki. Shooting him now would
> be against the Kshatriya dharma.” Krishna told him, “Satyaki has come
> here only to fight for you. How can you let someone kill him now? Save
> him.” **Arjuna said, “No. It is against the law.” Then Burishwara pulled
> out his sword in order to decapitate Satyaki. Again Krishna said,
> “Your friend, who put his life at stake for you, will be slaughtered
> now if you don’t reach out to him. Will you let him die like this?
> What kind of dharma is this?”** All this time, Arjuna’s arrow was aimed
> at Jayadrada. When Burishwara was about to decapitate Satyaki, Arjuna
> turned and shot the arrow at Burishwara. Burishwara’s right hand got
> severed. He looked around and said to Arjuna, “How could you do this?
> While I was fighting with another man, you shot me from behind and
> severed my hand? Anyone who has Kshatriya blood in him wouldn’t do
> such a dastardly act. I know you wouldn’t have done this by yourself.
> This cowherd with whom you are must have influenced you.” Arjuna’s
> anger flared up, and he said, “Yesterday, when you, a great warrior,
> joined many others to surround my son, a 17-year-old boy, and stab him
> from behind, where was your dharma? What are you talking about now?”
> Ashamed of the act that he had committed the day before, Burishwara
> put his head down. He went next to his chariot and sat down in lotus
> posture.</sub>

Abhimanyu was killed by cheating, while Drona was the Kaurava Army commander. If allowed, Drona ultimately would have got victory for Duryodhana, who was epitome of Adharma. This was the reason, Krishna advised Paandavas to lie.  
Ofcourse there would be bad fruit for such misdeed, which Yudhishtira had to undergo before entering heaven. But according to Krishna it was worth for establishing the Dharma.

[BG 18.66](http://www.vedabase.com/en/bg/18/66)  

    sarva-dharmān parityajya
    mām ekaṁ śaraṇaṁ vraja
    ahaṁ tvāṁ sarva-pāpebhyo
    mokṣayiṣyāmi mā śucaḥ
    

> Abandon all varieties of Dharma and just surrender unto Me. I shall
> deliver you from all sinful reactions. Do not fear.