High memory utilisation iPhone6: how to identify greedy apps/processes My iPhone 6 is constantly at around 98% memory utilisation, even when it is running a bare minimum two or three apps (these figures were obtained from the Lirum Info app).  The phone runs noticeably sluggishly, and it is not uncommon for apps to crash when attempting processor-intensive tasks.

How can I find out which app or process is consuming so much memory?  I wonder if there is one or more rogue processes which are out of control and should be killed?  Something akin to macOS Activity Monitor is what I'm looking for.

In an attempt to improve performance, I've tried all of the suggestions listed here, except a full backup and restore.  I am beginning to wonder whether an Apple iPhone 6 battery replacement may be beneficial, but before I do so, I would like to do some diagnosis to find out what the performance hog is.
One thing missing from your question is the age of your iPhone 6 or, more specifically, the age of your battery. My guess is that a battery replacement is in order as the symptoms just fit.

Also, the high memory utilisation is not likely to explain the symptoms your iPhone is currently having. An ageing battery, on the other hand (and ageing could refer to its cycle count instead of its age in time), is certainly one possible explanation for your symptoms. 

iPhone batteries are typically rated at having a maximum battery life of 500 cycles. However, this refers to the life of the battery and not to when you'll start noticing issues. In my experience, batteries can start showing signs of wear as early as when they reach about 65% of their cycle count and they start showing more serious signs at around 80% of their cycle count, so that's one figure you may want to investigate if you're still trying to make a decision.

It's not clear which version of the Lirum app you're using, but if you're only using the Lite version or aren't getting an indication of how many cycles your battery has had, you may want to consider coconutBattery (assuming you also have a Mac). 

coconutBattery is an awesome app that you can install on your Mac (if you have one). You can then connect your iPhone to your Mac and this app will show you the battery's current charge, its full charge capacity, and its design capacity, its cycle count, and so on. 

If you have a MacBook of some sort it'll give you a whole heap of info relating to your MacBook battery too.