What if Voldemort won the first war?
Voldemort goes after the Potters but instead of Lily, he gives James the choice to join his Death Eaters and let him through, James refuses and this provides the necessary sacrifice needed for Harry's protection. Voldemort doesn't kill Lily, instead he just stuns or otherwise incapacitates her until he deals with her son. Voldemort doesn't vanish after firing the killing curse but is weakened and retreats thinking the threat is eliminated. As per promise, Lily is spared and Snape is summoned to collect his reward prior to the Dark Lord retreating. While Lily refuses to leave her baby behind and fights Snape tooth and nail, they suddenly notice that the Harry is still alive. The killing curse did not actually kill him, he was only temporarily dead or only appeared to be like In DH. Obviously the dark Lord can never know of his survival. Snape uses a potion to alter Harry's features permanently and forges a new identity for the kid, the child of a Prince relative who joined the Death Eaters but was killed by the aurors. Snape took him supposedly in as he felt responsible for the last Prince and to make sure the kid is raised into a proper Death Eater.
Voldemort takes over the Ministry after recovering and tries to defeat Dumbledore. Things do not look good for the light, Dumbledore vanishes with the help of Fawkes and stays hidden until he can mobilize more order members. Sirius is still arrested and taken to Azkaban for openly defying Voldemort, Remus is on the run.
The wizarding world is under the control of Voldemort but he's not as insane as canon. He only kills those who openly defy him, he is keeping the statute still in tact for now but issues a lot of laws regarding muggleborns.
They're not threatened but obviously treated as second class citizens with limited education and limited job opportunities. Wizards and Witches are no longer allowed to marry muggles or muggleborns or procreate with them. Muggleborns are removed from their family after their first performance of accidental magic, their parents obliviated and the children given to Death Eater and Pureblood families to raise. They are practically homeschooled, not allowed to attend Hogwarts and are taught basic magic or specialize in whatever will serve their pureblood families. Essentially, they're a little above house elves. Hermione ends up with Severus and Lily and they teach her everything they can.
During the early years, Snape is forced to imperio Lily when Voldemort or the Death Eaters are present because he doesn't trust her to control herself. They don't question it, after all Snape needs her body not her mind. Snape later on convinces his colleagues that the events of 1981 and being under prolonged influence of imperio have damaged Lily's mind, she's no threat and believes Snape's "nephew" to be her dead son Harry. Should Voldemort ever look into little Harry's mind, this will be the explanation of any loving memories with his mother and why he is called Harry. Lily, has meanwhile, perfected the art of occlumency and impeccably empties her mind whenever the Death Eaters are present.
Snape is still involved with Dumbledore and helps him gather the Order members. Sirius breaks out of Azkaban and looks for Remus, they try to rescue Lily from Snape but she explains to them what is going on and reveals the Order's secret Headquarters to them. There are multiple assassination attempts against Voldemort but all miraculously fail, Snape infers that Dark Magic must be involved and Lily starts her research until she comes across horcruxes.
Let the hunt begin.
During the early years, Snape and Lily are a total mess together, Lily can't forgive him and believes he's enjoying this situation. They're constantly fighting but she settles down a little after realizing that she has no other choice but to stay with him. She later comes to understand Snape's true loyalties and their relationship improves. They may just have a platonic relationship or it could develop into something of a romantic nature later on.