restrict past dates in lightning:input

in your doInit function you have to set today date by using localization service for todayDate attribute.

like below cmp

 <aura:attribute name="todayDate" type="DateTime"/>

controller.js

 var timezone = $A.get("$Locale.timezone");
    var datetimestring =  new Date().toLocaleString("en-US", {timeZone: timezone}),
       datetime = new Date(datetimestring);
      datetime.setHours(datetime.getHours()+1);
    
    component.set('v.todayDate', datetime);

above solution works for me until summer20, after seen your comment i checked my project components all of them are broke. after all analysis what i found in summer20 release notes again. there is changes for lightning:input type=Date/datetime

The input types date and datetime have changed.

1.On the current month view of the date picker, you can now select a date from the previous and next month. Previously, dates from the previous and next month were disabled on the current month view unless you navigated directly to those months.

2.When you specify min and max values, users can still select a date outside of the min and max range. However, the blur event triggers the field to display a validation error message.

3.The names for months and weekdays in the date picker now use your Salesforce language setting. Previously, these names used your locale setting.

so in your case 2 point applied. that's why past dates are not disable. instead it giving the error.