I got it, just had to single quote the 01 in the Binary sensor.
#last Day of the month Sensor
- platform: template
sensors:
last_day_of_the_month:
friendly_name: 'Last Day of the Month'
entity_id: sensor.date
icon_template: "mdi:calendar"
value_template: "{{ (as_timestamp(now()) + 86400)|timestamp_custom('%d', true) == '01' }}"