Are you asking about conversational language or poetic language? There are English idioms that express when something is unconditional, or unlikely. But there's no English expression equivalent to "if the Sun were to rise in the West..." I'm going to trust the comments that this is a word-for-word translation of a Japanese idiom.
The way you translate idioms/poetry depends on what you want to achieve. If you just want a translation that sounds natural in a normal conversation, then avoid the expression entirely. You could replace it with an English idiom (only use idioms you're familiar with). Or in a lot of cases it's sufficient to say "I love you unconditionally," or "I would never tell a lie."
If you're writing a prose translation (borrowing a term from poetry), then the goal would be to translate the original Japanese as accurately and literally as possible. In those cases you would translate it as "if the Sun were to rise in the West..." Prose translations are normally made to help people understand the original Japanese text. You could translate everything like this, but it relies a bit on your audience already having a cultural understanding of Japanese. I'm not sure about the answer to your would/will question, because the Sun rising in the West is already such an unfamiliar metaphor.
However, if you're translating into poetic language, then you have more freedom to decide what features of the Japanese expression you're trying to translate into English. You could keep the comparison about the Earth's rotation, or you could use an English expression that feels similar, or reword the expression to sound more natural, understandable etc. You have to decide what's most important. No matter how you translate it, you're going to lose some of the original meaning. Some example poetic translations that try to keep the metaphor:
The Sun will rise in the West before I'll tell a lie.
The Sun may rise in the West; I will never tell a lie.
Even if the Sun rose in the West, I would still love you.
You asked about Shakespeare. Shakespeare quotes are instantly recognizable as poetic language, not conversational speech. There have been poetic translations of his work which update it to modern English. Although the most popular format of Shakespeare's work tends to be the original.