let lastYear = moment().subtract(1, 'year') ///так - отмотать на год назад

var str = "20.1.2020",
	parsStr = str.split('.'),
	lastDate = new Date( Number(parsStr[2]) - 1, Number(parsStr[1])-1 ),
	lastMountDay = new Date(lastDate.getFullYear(), lastDate.getMonth() + 1, 0);

console.log( lastMountDay.getDate() +'.'+ ("0" + (lastDate.getMonth() + 1)).slice(-2) +'.'+ lastDate.getFullYear() );

var 
  str = '29.11.2019'.split('.').reverse().join('-'),
  date = new Date(Date.parse(str) - 31536000000),
  options = { year: 'numeric', month: 'numeric', day: 'numeric' }
;

date.setMonth(date.getMonth() + 1, 1)
date.setHours(-1);

console.log(date.toLocaleString('ru', options));