From LimeSurvey Manual
Minimum date (date_min)
This question attribute can be used to set the minimum value for a date question (in y-m-d format or any English valid string - see below for more details). It can be used for both popup and dropdown display options. If a minimum date is not set, then 1.1.1900 is used as default.
- Any date value in format YYYY-MM-DD (eg., 2017-08-24);
- Any year value;
- Any English string : "now", "-10 years", "tomorrow";
- Reference to another date/time question : AnotherDateQuestion (using the question code);
- Expressions : With expressions, a minimum date can be dynamically calculated. For example, you can use a date from a previous answer + 3 days as a minimum for the present question by entering: date("Y-m-d",strtotime(departuredate)+3*60*60*24).