Задайте composer в dockerfile

RUN curl -sS https://getcomposer.org/installer | php -- --install-dir=/usr/local/bin --filename=composer

version: '3.7'

services:
  #...other services
  composer_installation:
   container_name: composer_installation
   image: composer
   volumes:
     - ./YOUR-PROJECT/:/app
   command: sh -c "composer install --ignore-platform-reqs && cp .env.example .env && php artisan key:generate"