Updating from core 8.7.9 to 8.8.0 I'm running into an issue when updating to Drupal core 8.8.0. I've removed both the vendor folder and the composer.lock file, as per instructions on this link 
https://www.drupal.org/node/2700999#s-special-considerations-for-upgrading-to-drupal-880-and-later

I run composer require drupal/core-recommended:^8.8 --update-with-dependencies
and I get the following:

  Problem 1
    - Conclusion: don't install drupal/core 8.8.5
    - Conclusion: don't install drupal/core 8.8.4
    - Conclusion: don't install drupal/core 8.8.3
    - Conclusion: don't install drupal/core 8.8.2
    - Conclusion: don't install drupal/core 8.8.1
    - Conclusion: don't install drupal/core 8.8.0
    - Conclusion: don't install drupal/core 8.8.0-rc1
    - Conclusion: don't install drupal/core 8.9.0-beta2
    - Conclusion: don't install drupal/core 8.9.0-beta1
    - Conclusion: don't install drupal/core 8.8.0-beta1
    - Installation request for acquia/lightning 4.0.4 -&gt; satisfiable by acquia/lightning[4.0.4].
    - Conclusion: don't install drupal/core 8.8.0-alpha1
    - Conclusion: don't install drupal/core 8.9.x-dev
    - acquia/lightning 4.0.4 requires drupal/claro ^1.0 -&gt; satisfiable by drupal/claro[1.x-dev, 1.0.0-beta1, 1.0.0-alpha5, 1.0.0-alpha4, 1.0.0-alpha3, 1.0.0-alpha2, 1.0.0-alpha1].
    - don't install drupal/core 8.8.x-dev|don't install drupal/claro 1.x-dev
    - don't install drupal/core 8.8.x-dev|don't install drupal/claro 1.0.0-beta1
    - don't install drupal/core 8.8.x-dev|don't install drupal/claro 1.0.0-alpha5
    - don't install drupal/core 8.8.x-dev|don't install drupal/claro 1.0.0-alpha4
    - don't install drupal/core 8.8.x-dev|don't install drupal/claro 1.0.0-alpha3
    - don't install drupal/core 8.8.x-dev|don't install drupal/claro 1.0.0-alpha2
    - don't install drupal/core 8.8.x-dev|don't install drupal/claro 1.0.0-alpha1
    - Installation request for drupal/core ^8.8.0 -&gt; satisfiable by drupal/core[8.8.0, 8.8.0-alpha1, 8.8.0-beta1, 8.8.0-rc1, 8.8.1, 8.8.2, 8.8.3, 8.8.4, 8.8.5, 8.8.x-dev, 8.9.0-beta1, 8.9.0-beta2, 8.9.x-dev].



At this point, running composer prohibits drupal/core:8.8.0 won't work because I removed drupal/core as per instructions in the link above.

I can successfully update to 8.7.13, so maybe I can settle for that for now. But our team wants to be ready for Drupal 9 and upgrading to 8.8 will make that transition easier, I hear.

Should I update to 8.7.13 first, before attempting to upgrade to 8.8?

EDIT 
I'm able to update to Drupal 8.8 by removing the vendor folder and composer.lock and removing acquia/lightning. I reinstalled acquia/lightning after Drupal core was added.
I am now running into issues when running drush dbupdate.
In your composer.json file (found in the root of your drupal site) find the line "drupal/core": "x.xx" and change it to "drupal/core": "~8.8" and then run composer update drupal/core --with-dependencies

Also, don't forget to run your database updates after! (run drush updb or go to your-drupal-site.com/update.php)