I cannot speak to evidence of Lehi's (or other's) journey to the western hemisphere, but as to "evidence" of Jesus teaching the western hemisphere peoples, there are the legends of the White God. All of the following excerpts come from "Four Peruvian Versions of the White God Legend" by Kirk Magleby (Tambuli,1 January 1984)
It is well-known that almost all Indian tribes in the Western Hemisphere preserve oral traditions about the ancient appearance of a white god who came down from heaven to instruct and organize his people. Some of the most interesting versions of this widespread tradition come from Peru, where this legendary deity is known variously as Kon Ticci Viracocha, Tunupa, Pachacamac, Tarapaca, or Arnauan, depending on the region of the country being considered. Four of the more highly acclaimed Peruvian historians, Pedro Cieza de Leon, Sarmiento de Gamboa, Betanzos, and Santacruz Pachacuti, have written especially interesting accounts of this white and bearded god, and when considered together, they give us a reasonably detailed description of the traditional hero’s physical appearance, personality, and activities among the ancestors of the Andean Indians.
Pedro Cieza de Leon arrived in Peru in 1548 as a simple soldier in a military group sent to quell an uprising that had turned into a civil war between the Spanish rulers of the country. He remained until 1550, during which time he visited almost every part of the newly conquered land, observing and recording descriptions of the terrain, the plants, the customs of the natives, and the major facets of their history. He had been keeping a journal of his observations ever since beginning his travels in Colombia in 1541, but now Cieza became fascinated with the idea of writing a history of Peru and its peoples. After completing his military duties, he would interview the amautas and orejones, the surviving wise men and noblemen of the Incas, as well as qualified Spaniards to learn all he could about the history and traditions of the conquered Inca empire.
“These things that I write here are true, and things of importance and benefit,” he wrote in the foreword of his first book, “because many times while the other soldiers slept, I wrote into the night until I wearied.” Cieza’s first work, La Cronica del Peru, was originally published in Seville in 1553, while the later El Senorio de los Incas remained unpublished until 1880. In chapter five of his Senorio, Cieza recorded the following legend about the appearance of a white god to the forebears of the Incas:
“Before the Incas ruled, or were even heard of in these kingdoms, these Indians speak of another thing much greater than all others which they tell, because they affirm that they went for a long time without seeing the sun, and, that, suffering tremendously with this deficiency, they raised great prayers and supplications to those they revered as gods, asking them to restore the light they lacked; and in this manner, there arose from the island of Titicaca, which is in the great lake of Collao, the sun shining brilliantly, which made them all very happy. And afterwards, they say that from the land of the noon sun, there came and appeared to them a white man of large build whose aspect and person showed great authority and veneration, and this man had such supreme power that he levelled the mountains and raised up the plains into large hills, making water flow from boulders; and since they recognized his supreme power, they called him the creator of all things, their originator, father of the sun, because even this notwithstanding, they say that he did many greater things, because he gave life to men and animals, and from his hand, they received notable benefit. According to the Indians who told it to me, who heard it from their fathers, who also heard it in the songs they preserve from antiquity; this man went towards the north, working many miracles in his journey through the mountains, and they never saw him again. In many places they say that he gave commandments to the men about how to live, and that he spoke with love and much humility, admonishing them to be good and not cause harm or injury to one another, but instead, to love each other and have charity. Generally they call him Ticiviracocha, even though in the province of Collao, they call him Tuapaca, and in other places he is known as Arnauan. Many temples were built to him in different places, where they erected stone statues in his likeness before which they offered sacrifices. The large stone figures in the city of Tiahuanacu are said to date from that era, and even though by tradition inherited from the past, they recount this that I tell of Ticiviracocha, they say nothing else about him, nor that he ever returned to any part of this kingdom.”
The journal and books of Cieza de Leon are oddly absent from most online discussions of these legends (e.g., Wikipedia's entry), which are primarily written to debunk efforts to link the legends to Ancient Aliens, Atlantis, etc. There are dozens of books on the subject and it appears most of them are tainted by the biases of the authors, some (if not many) of whom are not professional historians, archeologists, or anthropologists.
If we take these legends at their word, do they provide the proof or evidence you seek? No, they don't. There is striking similarity between the legends and the story found in The Book of Mormon, and the nature of religious dispute is such that the believers will always see corroboration and the dissenters will always wonder if Joseph Smith had access to copies of Cieza de Leon's works.2
But, there you have it to the best of my knowledge. If Cieza de Leon accurately recorded the legends and Joseph Smith's story is factually true, then they are evidence of Jesus Christ visiting and teaching the peoples of the western hemisphere some 1,500 years before Cieza de Leon's advent in the new world.
1 The Tambuli Magazine was the first LDS magazine in the Philippines. It was later replaced with the Liahona, which is the Church's magazine distributed outside the United States. When accessing archived magazines on the LDS Church's website, Tambuli will be found listed under the header Liahona.
2 Proving that Joseph Smith had access to Cieza de Leon's works is a good example of just how hard it is to prove the validity of any old or ancient text. In other words, it's just short of impossible to prove Joseph Smith had access to the books — but dissenters will always assume he did because, in their mind, it's impossible for Mormonism to be true and therefore there cannot be any proof. Likewise, believers will always assume he didn't because he couldn't have or he wouldn't have been a true prophet. Yuck. Now prove that any of the legends recorded by Cieza de Leon were (a) accurately recorded, (b) accurately interpreted, (c) not biased based on the changes in local culture over 1,500 years... and you see my point about how this is interesting, but hardly proof.