You can manage the Joomla site on the site level by enabling debugging and seeing what's occurring on the pages if we're talking about Joomla 3.x. From there, you can make any adjustments necessary(reworking queries, trimming out offending extensions, etc).
You should also be able to get a more involved look at the situation in real time using htop through SSH, which will not only tell you about running processes, but in most cases, what precisely is running. You can achieve similar results with the "sar" command, but a perk to this will also give you the server's "trends", especially useful if you're on a dedicated hosting environment.
Of course, if all else fails, you can permit the account for additional resources under LVE. I don't know to what extent your site is consuming memory, so I can't say if it would be "too much" for your situation. CloudLinux on base configuration initiates extremely conservative limits on accounts.
If you are not an admin on the server but are using cPanel, raise the concern with your host and see if they can get you any of the information mentioned previously(you could also mention that you're experiencing these memory spikes and want to know what's going on, most of the time they can help pin-point the issue but unless they know anything about Joomla, they may also tell you something that doesn't quite make sense and could be potentially incorrect).
You may have a plugin called "Resource Usage" or "Resource Usage Details" on your cPanel home screen, if not, I'm sure your host would be happy to install it. This way at least you have that information available in the future and won't have to wait on a response from the host to really get into troubleshooting.