I think there are two separate problems here.
If I'm not mistaken, what mainly drives the RAM usage in Adobe Media Encoder would be the pixel dimensions of the frames being processed. I think it's unlikely that it would get anywhere close to needing 60GB of RAM using a typical 4K project.
The lagging with 4K is probably a separate issue that may be due to the combination of CPU, storage speed, and graphics hardware. The i7 CPU seems OK, and there is more than enough RAM.
The hard drive is a suspect; although it's a good model, it may not be able to play 4K frames fast enough on a video timeline if the system and Premiere Pro are simultaneously making requests of it. Especially for 4K, it would be better to store the OS, the footage, and the Adobe media cache each on a separate drive so they can be accessed in parallel, and it would help a lot more if at least one of those drives was an SSD, which is many times faster than a hard drive.
In short, a single hard drive is not ideal for 4K editing.
What graphics hardware is in the computer? A card, or integrated graphics? 4K editing is smoother when the graphics hardware is supported for Mercury Playback Engine acceleration in Premiere Pro.
Even then, on a lot of systems, smooth 4K editing is only practical using a proxy workflow. My computer is older, so the only way I can quickly edit 4K is to use Premiere proxies.