We have some processes / triggers / workflows setup to do some updates on child accounts and contacts once you update a certain field. For example, if you update the email field in the account, the "person in charge email" field on the child accounts and contacts also updates recursively down the whole hierarchy.
I did an update on an account with 2000+ contacts in Salesforce Classic and got the "Apex CPU Limit time exceeded" error message.
Now on "accident"(because the org still uses Classic when I'm sometimes working in Lightning already) I've tried the same update again in Salesforce Lightning and the update went through without a problem.
Are there different limits in Lightning and Classic or how can we explain this behaviour?