From what I've read, people with LLE on its own thread never have the problem of it causing the bottleneck. The CPU I see recommended most often is the i5 2500K, as it is fast, cheaper than an i7, and is the only overclockable Sandy Bridge i5. Also this CPU is pretty much going to be sufficient for any task, as Dolphin doesn't use more than 3 cores, and few people need more than four cores/threads for anything. However you'd do slightly better with a far more expensive, slightly faster, overclockable Sandy Bridge i7, but for the price difference it isn't worth it.
OS: Windows 10 64 bit Professional
CPU: AMD Ryzen 5900X
RAM: 16GB
GPU: Radeon Vega 56
CPU: AMD Ryzen 5900X
RAM: 16GB
GPU: Radeon Vega 56
