Lizardfolk Pc makes no sense every townguard would immidiately attack you and you would certainly have no chance to get into Baldurs Gate itself.
You really need to buy Baldur's Gate: Descent into Avernus if only for the Baldur's Gate Gazette inside. It straight up mentions Lizardfolk are living in Baldur's Gate, and in Volo's Guide to Monsters Lizardfolk aren't concidered a monster race, unlike Gobliniods, Orcs, Yaun Ti Pure Blood, Kobolds which while playable are concidered monster races. Most Lizardfolk society is on its own neutral and not evil. In fact as long as one is not disruptive, monster races and fiend worshipping cults are tolerated, especially in the Outer districts (Baldur's Gate is very Lawful Neutral, almost leaning towards Lawful Evil behind closed doors). Heck even the Drow operate openly in cities along the Swordcoast. Both the Spellplague, the Sundering, and other events shook society enough that xenophobia in most places is less stabby and more social, outside of really extreme cases.
Plus doing deals with various tribes is not unheard of. Until rescently they even traded with the Orc nation of Many Arrows.
