I don't think performance of PHP itself will be a problem. Hard to say much else helpful without more detail though. I've got a large PHP app running a fairly big lab (ballpark £100m facility) running on a 7+yr-old bottom-of-the-range server and it barely ticks the cpu - in the process of migrating it to laravel and performance overhead is the very least of my worries ;-)
This would require handling subdomains per accounts, multiple DBs per accounts for HIPAA compliance.
I love the ease of Laravel and how powerful it is.
It has to handle over 5k daily users in 100s of different labs all over the US.
It also has to be modular to add components later.
In reality there is 3 sections Admin (for setting up the lab) Lab Portal (for lab result tracking and so on, and the Portal (Doc offices for getting results and such).
It may not sound large at first, but I keep thinking future growth.
For heavy hitting you should use compiled c++ classes. Study how facebook deals with heavy hits. Short of that I would consider java technology namely servlets / jsp / hibernate combination. Php is not large enterprise. Some large enterprise still use php for low level stuff, such as a customer portal. They leverage multi technologies.
But dealing with more records in a week than most on the forum deal with in a lifetime, not php alone.
@jcomee I don't think the language you use will be a bottle-neck for you. You can always proto-type using laravel and then see how it feels. If there's something that turns out to be a problem then you can adjust. 5k users a day isn't a lot in itself - it'll depend what those users are doing. If they want to upload a terrabyte of DNA sequences and process them in the browser - then that's a problem ;-)
From my experience with lab-related things it's more likely to be nasty DB+calculations for reports/stats, handling large file uploads/storage, privacy/encryption etc than which language the http layer is in. Tackling those is often quite case-specific - depending on what it is maybe you end up with some python back-end stuff for stats/bio/infomatics, fiddling about with LUKS, or if you're very unlucky like me then you have to include some TCL too ;-)