It is a beautiful day for a picnic by the lake in the central park is a complete and correct sentence. It explains when an action takes place that is today which is regarded a “beautiful day” and where the action is to take place “by the lake in Central Park”.
It is the beautiful dayis not correct because of the word “the” it makes the sentence an unspecified sentence.
“Let’s go on a picnic” sounds like a complete statement but it’s not definite of where and when this action should take place.
It is a beautiful day for a picnic by the lake in central park.-a is not correct because beautiful day is unspecific. you could use the in this sentence if you indicated which beautiful day you meant, as in:it is the beautiful day i hoped for yesterday.b is not correct because it does not include the indefinite article a before park.c is incorrect. the a is used correctly before lake but you dont need to use an article before a proper noun such as central park because it is a name of a specific park. you could use the in the sentence if you removed the name of the park, as in:is there a lake in the park?d is correct.