NJ - How to get rid of tenant at end of lease?

[Tim Dastis]

I purchased my first rental property (triplex) 7 months ago and have had pretty good success with it thus far minus a few hiccups here and there.  

In my one unit however I have trouble tenants who are habitual late-rent payers.  I probably have been too lenient but with juggling 3 units plus purchasing a new primary residence that needed major renovations I was a little hesitant to evict.

Regardless, here we are again nearing the first of the month and the excuses are coming in as to why rent is late.  With 4 months to go I'm not sure if it's even worth it to evict (they have 5 business days per my lease until it is late, so that's June 8 and it may not come to that).

My question really is how to end the lease and make the tenants move out.  I had a RE lawyer write my lease but it doesn't really say anywhere about non-renewal.  Here is my language:

So I could really use some guidance as to how to send a notice, let them know, etc that I do not wish to renew the lease with them and request that they move out at the lease end date, 9/30/17.  Any advice at all is greatly appreciated.  BP has been a great resource for navigating my first property!