What LCP actually measures
Largest Contentful Paint records when the largest text block or image in the viewport finishes rendering. It is a proxy for the moment the page looks useful, and Google treats 2.5 seconds or less as good, measured at the 75th percentile of real visits.
Because a hero image is usually the largest element, LCP is often just a measure of how quickly one image arrives and decodes. That breaks down into four parts: how long the server took to respond, how long before the browser discovered the image, how long it took to download, and how long to render it.
Compression attacks the third directly and the fourth slightly. Preloading and fetchpriority attack the second. If your problem is the first — a slow server — no amount of image work will fix it, which is why it is worth measuring before optimising.