I am using Google Kubernetes Engine and have the Google HTTPS Load Balancer as my ingress.
Right now the load balancer uses Let's Encrypt certificates. However, is there a simple way to ensure that the certificates are automatically renewed prior to their 90 day expiry?
You can now use "Google-managed SSL certificates" which is currently in beta: https://cloud.google.com/load-balancing/docs/ssl-certificates#managed-certs
You have not specified how you configured Let's Encrypt for your load balancer. Right now Google does not offer this for you, so I assume you mean you set the Let's Encrypt certificate yourself. In this case, Google can't renew your certificate.
Until there's an official support you can install a third-party add-on like cert-manager to automate certificate configuration and renewal. There's a GKE tutorial for doing this at https://github.com/ahmetb/gke-letsencrypt.