Pension Lump-Sum refund, and missed payments

I am currently getting ready to move out of Japan. I have been paying into the pension system consistently for a number of years now, but became slack over the past few months for various (obvious) reasons related to the fact that moving is expensive and that I'm leaving the country.

I just went to City Hall to complete the moving-out process, and the office slapped me with a bill for the 4 months of pension I've missed, and asked me to pay it at a conbini before I leave.

My question is, would these few recent missed payments affect my ability to claim the Lump-Sum withdrawal that I plan to apply for once I'm back in Canada? Do I have to cough up $500 more dollars before boarding a plane in order to get my refund?

city offices collect payments from individuals, and 日本年金機構 pays refund and benefit.
you can ask it at the nearest 年金事務所 of 日本年金機構.
https://www.nenkin.go.jp/section/soudan/

On my understanding (having looked at this earlier in the year for someone), I would say yes. Your refund is based on payments over the last year, not how long you've been paying, so any recent missed payments would have a big effect.
That was my reading of the guidance, might be wrong.

Thanks so much for your help, everyone! Very much appreciated!