It will depend on how one understands avatar, most literal and religious ideas fall quite short. It can be made simple. Buddha simple means awake and sri vishnu means to pervade all of space akash and beyond into vaikuntha which has unlimited lokas, Saketa is an ancient name of ayodhya, realm of Raja Ram tri loka nath~peaceful ruler of prajna~wisdom, and ten directions manas~mind 5 jnanendriyas and Karmendriyas~ 5 media senses, all vaikuntha lokas are all of the nature of supreme peace free from dukkha and rebirth, space is akasha which is the universal realm of Brahmanda or the inner universe. Neither Buddha or sri Vishnu are visible in the outer universe, only in a limited way that texts and deities are made, these are mediums only or the bhagavat, living example of Brahman, all auspicious Sadasiva.
What pervades all of space akash is awaking the chitta, sun and moon, expansions of brahman, buddha awakens the citta, citta in vak was known as a follower, it either follows the outgoing tendency of desires into becoming and becomes under control of the external or it follows and grows expands into the akash and becomes enlightened bodhi from Buddha which exists in all pervading space. Sri Vishnu lower garments is akash.
The later translations that Sri Vishnu incarnated as Buddha to trick the atheists and turn them against the vedas is purely fictional and a purpose fabrication of the texts to divide the dharma traditions, by anthropomorphic monotheistic materialists, who operate in forums to keep the divisions alive. vedas themselves are not a body of texts, although there is textual scripts, which practical no human being can translate, the way of grammar is a false construct, and artificial means.
Veda is is combination of sound and light, nada and joyti, expansions of chandra and surya, Mogallana and Sariputra, , which are experienced in space of consciousness chid akash, what precedes scriptural texts is sandhi, this is the middle way, supramental realm, madhyamika, sunrise and sunset, the marriage of balanced of the extremes day and night, sama. If these things are brought into religious belief then you fall for the trick of the pen, fall for the trick of being controlled on the outside, speech of men manas mind born theories, if you identify yourself as Buddhist then its either of one of two things, its a belief, where belief has not role in abhidharma, or you claiming to be an enlightened being, where no such claims proposed by an individual. Buddha in the sutta sutra su transcendent and tra vibrations are the middle way, the threads to beyond birth and death, becoming and fading.
Scholars and religious believers make a mess of the whole thing, just chant suttas and vibrate and knowledge comes, its easier than people think, but they think discussing is the final way to make something real, its just another limited form of empiricism. Ones who citta has not turned inwards will not see these things in their own practice. Most traditional and institutional practices are corrupted to keep dependency on the outside.
The Rig Veda 1.164.45 says “catvari vak parimita padani tani vidur brahmana ye minishinah, guha trini nihita neengayanti turiyam vaco manushya vadanti” (i.e. The cognoscenti know of the Vak that exists in four forms . Three are hidden and the fourth is what men speak) .
Exploring Theravāda's connections to other paths - what can we learn from other traditions, religions and philosophies?
Lord is not the correct the word, visnu vi inner ruler~antariyami ekantha, Vishvarupa of the cosmos brahmanda, supramental realm, is always accompanied with sri, devi, mahamaya, she is anugraha grace prasade of visnu ~ vishuddhi sattva tattva, so is addressed as sri vishnu. Sri is laxmi bringer of all wealth and Vidya, vid cognitive knowledge, ya~manifestation or appearance, with all good fortune laxmi devi Sri Vidya, vid is light or illumination of veda, combination of nada sound and joyti light in brahmanda, brahmanda is pieced through brahmarandra with avatars of visnu, rudras of shiva and shakti, This the discovery of Buddha ( awakened ) is the recognition (sañña~Saṃjñā), of Tathāgata ~ Sugata~Brahman