Clearance between SMD components
You haven't given a part number for your LEDs, but the datasheet should tell you this information.
As an example, look at this excerpt of a datasheet:

You can see that for each dimension there is a 'MAX' column. You simply need to ensure your component placement respects this with regards to the LED package outer dimensions.
Sometimes you may see a global tolerance on dimensions rather than a nice table like this.
I like to make my component silk outlines to the package maximum tolerances rather than the nominal. That way I can place them right up next to each other in the PCB capture software without having to worry.
Edit: Please also see @dim's excellent comment about some assemblers having a process requirement for component separation. So, check your component maximum package size tolerances and check that your particular assembler does not have a process limitation.