Hi John! Thanks for reaching out. There is now a way to apply conditional formatting across multiple sheets within the same document as you are describing.

If you open up Conditional Formatting on the right bar while on another page of the same doc you will see that it is applied to selected shapes (it will tell you the number of shapes it is applied to on the current page you are on in the screenshot below that being 0/16). You can then select the shapes (or chose all shapes) that you would like to apply it to on that additional page. There is no need to create a new rule for each page of the same document!

Let me know if you have any other questions about this!

Hey have you added this feature in yet? I really need to be able to apply conditional formatting rules across multiple documents. 

Hi Jake Thanks for following up of this! Yes conditional formatting rules can now be applied to multiple pages within the same document (please see revised comment above for details on how to do so).

However there is not a way to apply conditional formatting rules across separate documents. We are always looking for ways to improve Lucidchart and your feedback is the best way for us to do that. Would you mind adding your idea to our feature request form?