Can I use Famipay in Lawson?

Yes, you can.

The steps used in other stores are:

1. Launching FamiPay App.
2. Tap the 「ファミリーマート以外で使う」 button.
3. Have the clerk scan the barcode.

That's all.

But I must say, you can't pay separately. You can only choose one payment method. 

At Family Mart, you can use two payment methods (Famipay+Cash) to pay, especially when your balance of Famipay is insufficient.

You can check the link below for details.

References:

ファミペイなのにローソンOK！使える店・メリット・始め方を解説！