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" is on the same event but different aspect. Its source 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. 1
1: This verse is omitted in the Bombay text. There can be no
doubt, however, about its genuineness.
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 during Jayadratha Parva:
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
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.
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.