My first inclination is that the Livewire isn't ideal for your commute, if you genuinely have no ability to charge during the work day.
I think you probably would have enough range to make the trip when the bike is new. However, as the battery gets older your range will decrease. This decrease doesn't mean a lot for people like me who use the Livewire as a city bike/weekend toy, but if you are using the bike for a lengthy commute it might not be sufficient after a few years.
That being said, do you have any opportunity to charge at work? The commute you describe won't need fast/level 3 charging. A standard outlet will add about 10 miles (16 km?) per hour of charging ( side note: I think your voltage is 240 as opposed our 120 volt standard, although I understand the Livewire charges at the level 1 [120 volt] rate even when it is plugged in to a 240 volt outlet?). So if you are able to find an outlet to plug into while you work, the range of the 'Wire will be more than adequate.
So, if you want an excuse to buy a Livewire AND you are able to plug in at work, I'd say go for it. If your employer sucks and doesn't allow you any opportunity to plug in, the bike might not meed your needs.
I hope you are able to find a way to charge at work. The 'Wire is an extraordinarily fun bike to ride. I've enjoyed every minute riding it, and I think you will too.
