If you're looking for stability over a long period of time, for a large app or otherwise, you have to weigh your options.
An app that has a long shelf life may better suited in something else, keeping in mind that you won't get the latest greatest updates/features. Having access to the latest is nice but it's also overhead work to keep up with the changes.
If there is a certain case where you can't simply update the framework and tech stack, or the app will sit for a long period of time (a la Enterprise), these type of scenarios would favour an LTS. A year goes bye in a blink in a large environment. Depending on your situation an LTS could be beneficial. Business partners don't want to hear that their investment goes down the tubes and they're vulnerable to security holes because the framework shut down since one guy was running it. They are buying stability. Some are ok with the risks of using the latest, but business leaders need to understand overhead involved in continued changes and have a plan for a scenario as described above.
Here are some options that might be more suitable to LTS.
In PHP, Symfony has LTS support:
http://symfony.com/roadmap
Version 2.7 (being released May 2015) will be supported by bug fixes until 2018 and security fixes until 2019.
Symfony is operated by http://sensiolabs.com/ - a commercial entity. They offer services supporting Symfony but if SensioLabs were to fail I don't know what would happen to Symfony. Symfony components (not the framework) are used in some of the largest open source PHP apps available today, including Laravel, so I would assume they would continue to be supported.
If we look into other languages and comparable frameworks:
In Python, Django 1.8, just released this April, supports 3+ years of support (2018).
https://docs.djangoproject.com/en/dev/internals/release-process/#lts-releases
Django seems very mature in this space, has a Django Foundation supporting the framework, and Python is very organized with the Python Software Foundation. Well documented and considered proposals via Python Enhancement Proposals (PEPs).
To my knowledge Ruby on Rails does not offer LTS support.
I'd avoid Node.js since the environment is rapidly changing.
Java EE has some well supported LTS type releases but requires a different mindset and, in my opinion, has higher overhead than PHP or Python.