TL;DR

I couldn't find the connection to Lalitavistara so far either.

But Hindu-leaning pages like this seem to popularize the idea that Buddhist literature denigrate the Hindu deity Krishna, when it actually does not.

Kanha in Pali is Krishna in Sanskrit.

And the term Kanha in Pali literature is mainly used to refer to Mara, the Evil One or Dark One who is the temptor, probably the same person as the Hindu Kamadeva (cupid).

It also refers to Vasudeva, probably the same person as the Hindu deity Krishna. Vasudeva is identified as the past birth of Sariputta, the Buddha's chief disciple.

For what it's worth, Vasudeva (aka Krishna, Kanha, Kesava) is different from Mara, the Evil One.

And if you read further, you will find that the Vasudeva stories from Pali literature may not match exactly with the Krishna stories from Hindu literature.

Details:

From the footnotes of Padhana Sutta:

The "Dark One" or Kanha (Sanskrit: Krishna), is another name for Mara. He is the Indian Cupid (Kamadeva) and personifies sensual passions. He carries a lute (vina), mentioned at the close, with which he captivates beings by his playing. His other equipment includes a bow, arrows, a noose and a hook.

And from Palikanon's dictionary of proper names on Mara:

Generally regarded as the personification of Death, the Evil One, the Tempter (the Buddhist counterpart of the Devil or Principle of Destruction). The legends concerning Māra are, in the books, very involved and defy any attempts at unravelling them. ....

The later books, especially the Nidānakathā of the Jātaka Commentary (J.i.71ff.; cp. MA.i.384) and the Buddhavamsa Commentary (p. 239f), contain a very lively and detailed description of the temptation of the Buddha by Māra, as the Buddha sat under the Bodhi tree immediately before his Enlightenment. These accounts describe how Māra, the devaputta, seeing the Bodhisatta seated, with the firm resolve, of becoming a Buddha, summoned all his forces and advanced against him. .....

There is no doubt that the Māra legend had its origin in the Padhāna Sutta. There Māra is represented as visiting Gotama on the banks of the Nerañjarā, where he is practicing austerities and tempting him to abandon his striving and devote himself to good works. Gotama refers to Māra's army as being tenfold. The divisions are as follows:

• the first consists of the Lusts;
• the second is Aversion;
• the third Hunger and Thirst;
• the fourth Craving;
• the fifth Sloth and Indolence;
• the sixth Cowardice;
• the seventh Doubt;
• the eighth Hypocrisy and Stupidity;
• Gains, Fame, Honour and Glory falsely obtained form the ninth; and
• the tenth is the Lauding of oneself and the Contemning of others.

Māra bears many names in Pāli Literature, chief of them being Kanha, Adhipati, Antaka, Namuci and Pamattabandhu. (MNid.ii.489; for their explanation see MNidA.328; another name of Māra was Pajāpati, MA.i.28). His usual standing epithet is pāpimā, but other words are also used, such as anatthakāma, ahitakāma, and ayogakkhemakāma (E.g., M.i.118).

The name Kanha can also refer to the Hindu deity Krishna I suppose, as Vasudeva.

1. Kanha.-A name for Māra. E.g., Sn.v.355; M.i.377; D.ii.262; Thag.v.1189.

2. Kanha.-The name of the Bodhisatta; he was born in a brahmin family and later became a sage. He is also called Kanha-tāpasa, and is mentioned among those the memory of whose lives caused the Buddha to smile. See Kanha Jātaka (2). DhsA.294, 426.

3. Kanha.-Another name of Vāsudeva (J.iv.84, 86; vi.421; PvA.94ff ); the scholiast explains that he belonged to the Kanhāyanagotta.

4. Kanha.-Son of Disā, a slave girl of Okkāka. He was called Kanha because he was black and, like a devil (kanha), spoke as soon as he was born. He was the ancestor of the Kanhāyanagotta (D.i.93). Later he went into the Dekkhan and, having learnt mystic verses, became a mighty seer. Coming back to Okkāka, Kanha demanded the hand of the king's daughter Maddarūpī. At first the request was indignantly refused, but when Kanha displayed his supernatural powers he gained the princess. D.i.96f.; DA.i.266.

5. Kanha.-A Pacceka Buddha, mentioned in the Isigili Sutta. M.iii.71.

6. Kanha.-A dog. See Mahā-Kanha.

7. Kanha.-See Kanhadīpāyana.

The entry on Vāsudeva states:

The eldest of the Andhakavenhudāsaputtā.

The Ghata Jātaka (No. 454) relates how, when Vāsudeva's son died and Vāsudeva gave himself up to despair, his brother Ghatapandita brought him to his senses by feigning madness.

Vāsudeva's minister was Rohineyya. Vāsudeva is addressed (J.iv.84; he is called Kanha at J.vi.421) as Kanha and again as Kesava. The scholiast explains (J.iv.84) that he is called Kanha because he belonged to the Kanhāyanagotta, and Kesava because he had beautiful hair (kesasobhanatāya). These names, however, give support to the theory (see Andhakavenhudāsaputtā, No.1) that the story of Vāsudeva was associated with the legend of Krsna.

In the Mahāummagga Jātaka (J.vi.421) it is stated that Jambāvatī, mother of King Sivi, was the consort of Vāsudeva Kanha. The scholiast identifies this Vāsudeva with the eldest of the Andhakavenhudāsaputtā, and says that Jambāvatī was a candalī. Vāsudeva fell in love with her because of her great beauty and married her in spite of her caste. Their son was Sivi, who later succeeded to his father's throne at Dvāravatī.

Vāsudeva is identified with Sāriputta. J.iv.89.

And finally the entry for Andhakavenhu-(dāsa)-puttā gives us the Hindu Krishna story, more or less:

Ten brothers, sons of Devagabbhā and Upasāgara.

As it had been foretold at Devagabbhā's birth that one of her sons would destroy the lineage of Kamsa, each time a son was born to her, fearing lest he be put to death, she sent him secretly to her serving-woman, Nandagopā; the latter had married Andhakavenhu and, by good fortune, daughters were born to her at the same time as sons to Devagabbhā; these daughters she sent to Devagabbhā in exchange for the latter's sons.

The ten sons were named Vāsudeva, Baladeva, Candadeva, Suriyadeva, Aggideva, Varunadeva, Ajjuna, Pajjuna, Ghatapandita and Ankura. Cowell sees in this story the kernel of a nature-myth (Jātaka, trans. iv. 51 n. ); cf. with this the Krsna legend in the Harivamsa; see also Wilson's Visnu Purāna (Hall's Ed.), v. 147f.; and the article on Krsna in Hopkins' Epic Mythology, pp.214f.