You do not need a temporary membership to crew at EMRA events. Some tracks like to have your name on an advance crew list at the gate but I have not seen Lime Rock do this.
It is is best to register your car as early as possible. Some of the folks that do registration and tech are also involved in other duties once the racing starts. It's not impossible to register a car at mid-morning and run an afternoon race....but it can be kind of a hassle for everyone. It's much better to get to the track early and get your car all squared away so you can focus on enjoying the event.