How do I get my landlord to give me a lease?

Long, stupid story, but here it is: My fiance and I have lived in our rental house for a little over a year now with our dog, cat, and goats. Upon move in we were told the lease would be imminently forthcoming, and brought this up at the one month and two month marks. Then I gave up nagging and it hasn’t really been an issue until recently, when I asked permission to adopt a new puppy. Landlord refused, stating that our lease actually states “No pets.” Ok, says I, that’s kind of odd given that it’s never been brought up before, plus I know the last two renters had pets too, but fine, whatever you say, – but can I please get a copy of the lease now, so we are on the same page about stuff like this, and so we can write in my current animals for personal liability purposes. But wildpotato, he says, we’re not going to pull any funny stuff with you. Ok, I reply, but it would just make me more comfortable to get things down in writing. He finally agrees but claims that the lease is located on a computer they need a new battery for, so I ask for a timeframe for when he can get it to me. A week, he says.

It’ll be a week tomorrow. I am 99% sure that he will not have the lease ready, nor will even bring it up of his own accord.

I feel like I’m living in Bizzaro-world here – how is it possible that a landlord wouldn’t want to do this? A few more details to set context for this crazy situation – he and I had been on friendly terms up until a few months ago, when he refused my requests to fix the mailbox (there’s still no door on it) and to plow the driveway or arrange to have it plowed by a reasonable time following heavy snowfall (this is a requirement for landlords in my state). Now he seems to expect me to continue our business relationship based on a goodwill that I no longer believe exists between us. I shouldn’t have had to rely on it from the get-go, I know, but this is a small town and I trust too easily. He and I are still on friendly speaking terms, but I am no longer willing to trust him, since it’s become clear that his thoughts and intentions are absolutely opaque to me.

Is withholding the rent my only arrow in the quiver? Or having a lawyer contact him? I really, really don’t want to go there, especially because 1) I’m friends with the rest of his family and the last thing I want is to fuck them over, and 2) I’m not prepared to move right now. Any ideas? – the less acrimonious, the better. Is there any friendly way to go about this?

Tl;dr: I’ve been living in my rental lease-free for a year and am no longer willing to let the situation stand. Is there anything I can do other than withhold rent to extract a lease from my landlord?