I think a better criterium for "peak years" is peak momentum (user increase over time), vs peak users.
Most technologies reach peak users when they stop growing or when their growth stops accelerating (and then they either get somewhat stable -e.g. Microsoft, or like many, start to decline - e.g. Blackberry).
Limewire's peak years were immediately before settling a lawsuit. When the lawsuit threats started, the owner panicked, put out a press release saying that he would shut down the company right away, then back-peddled and announced he'd fight the lawsuit. There was a ton of noise in the press and lots of media speculation about what was going to happen, which generated tons of free advertising.
Part of the settlement was using the auto-update feature to update the vast majority of users to a record-label-developed application that was skinned to look like LimeWire. (I left a year or two before the killing update, but as I remember, they made one release that removed the optionality from the auto-update, waited for the majority of users to update, and then force-updated everyone.)
LimeWire's fall in popularity didn't look anything like a normal decline.
I don't think the media frenzy free advertising was intentional, but the owner was a bit of a mad genius. He has tons of ideas, 80% of which are batshit crazy, and 1% of which are out-of-the-box brilliant. He has a few people close to him who are good at picking out the uncut diamonds. He also founded and runs a very successful hedge fund. On the other hand, he emailed everyone a paranoid email and then talked to journalists about it when it leaked[0].
Most technologies reach peak users when they stop growing or when their growth stops accelerating (and then they either get somewhat stable -e.g. Microsoft, or like many, start to decline - e.g. Blackberry).