Speak to the leasing company – none of them will want you to take it to the legal limit – I forget the actual figures but when I worked for Lombard VM the limit was something like 1.6mm and we’d allow tyres to be changed at 2.5mm. There were also unpublished ‘fair usage rules’ regarding how many tyres you could have – I only ever saw them imposed once though when some bright spark leased a Nissan 350Z and wanted a set a month, we was using it for track days.
Anyway, most of the tyre fitters no the score, they don’t get paid for calling the lease company and telling them you’ve got plenty left, they know what to say.