The NIP will go to whoever is currently the registered keeper, most likely the lease company. they will reply to it naming your company as the driver. your company should then reply to the nip naming you as the driver. It sounds like your company just handed you the NIP to deal with, which is illegal.
For your second NIP, the fact that you were named on the first one makes no odds, it will go to the lease company again and so on. The system will not look at the reg number and go "ooh, that ended up with Currymonster last time, I'll send it straight to him this time".
Also the 14 day rule doesn't apply to you. It only applies to the first NIP, ie the one to the lease company. The lease company then have 28 days to reply and the ticket office have 28 days to issue a second NIP, and so it carries on.
In theory if it does go Lease -> your work -> you, it could take up to 126 days to reach you and still be within the time limits.
If you're going to try and fight it, pepipoo.com is likely a better site for you. SafeSpeed is more about trying to get the law changed to something sensible rather than helping people break the current law.
That said, I'd visit the site and check for one of the following:
1) a built up area with streetlamps no more than 84 metres (100 yards) apart
2) 30mph repeater signs at regular intervals
If neither of these are present then the 30 limit is invalid and unenforceable. There are other signing and lighting regulations too (such as needing to have

signs on both signs of the road at the start of the 30 limit and for them to either be lit or be within a certain distance of a streetlight) but the above two are the most common ones for a 30 limit being invalid.