Google hasn't officially made any announcements about what watch hardware will receive the Android Wear 2.0 update when it's released later this year, but it looks like at least a few of the first-generation watches will be missing out. LG says it has no plans to update the original LG G Watch, and now Motorola says it plans to drop support for the original Moto 360. Given Samsung's disinterest in continuing on with new Android Wear hardware, the future doesn't look rosy for the Samsung Gear Live, either. This news comes just two years after Android Wear and many of these watches were originally introduced.
The Moto 360's hardware was always underpowered even when it was brand-new, but the LG G Watch uses the same Qualcomm Snapdragon 400 SoC that many newer Wear watches have included. As is usually the case with Android phones, your OEM's willingness to provide updates for hardware it has already sold you has more to do with whether you get updates than your actual hardware does.
Many Android Wear updates, version 2.0 included, have added features that require new hardware components—support for Wi-Fi, internal speakers, LTE, and more has all been added since these first watches launched, and only more recent watches have included the necessary hardware in the first place. Those watches will continue to work for the foreseeable future, in all likelihood. But all of the other software improvements, including the redesigned interface, security updates, and other tweaks, will be skipping your wrist unless you pay for something new. If that's what you decide to do, make sure the watch's manufacturer has committed to updating its software first.