Prep the watermelon by cutting or scooping out the flesh. Add the watermelon to a blender with the lime juice and sea salt, if using. If it does not all fit, fill the blender about two-thirds full, blend briefly, then add the remaining watermelon.
Blend for 45-60 seconds, or until completely smooth. Use a blender tamper if necessary to get the watermelon moving. Taste and add a little more lime juice if desired.
For completely pulp-free watermelon juice, strain it through a nut milk bag or fine-mesh strainer. Straining is optional. If left unstrained, stir or shake the juice before serving because natural separation can occur.
Transfer the juice to a jar or pitcher and refrigerate until chilled. Alternatively, serve immediately over ice.