how does LBO analysis imply a share price?

Usually share price is irrelevant because you're placing a purchase price on the business itself as a whole so I don't really understand your question.

In a lbo model, equity price is more of an assumption than a result. By assuming an equity price, you can calculate what kind of level of debt (and in what form) the business can sustain

You run analysis based on finding an EV range that satisfies returns bogey. Once you have a range of transaction values, you know your min and max purchase price that makes the math work. From EV, you can calculate equity value, and thus, price per share.

The share price is an input to the lbo model, you have to model in an assumption for the price you pay to buy out current equity holders (whether public or private) in order to calculate IRR.

If you are a PE firm, you are asking yourself how much am I willing to pay for the business (Enterprise value) and then from that you determine what you'd be paying to the current equity owners. If it's public you'd be looking at what share price that analysis implies.

If you are doing an LBO analysis for the purposes of valuing a company, you would think the same way as the PE firms - you would calculate the EV and thus equity value that would allow a sponsor to earn an acceptable return.

In an lbo model, equity price is more of an assumption than a result. By assuming an equity price, you can calculate what kind of level of debt. You can try some good videos for a clear picture. I can recommend Bluebook Academy..