The second sentence is correct :)

Only choice 1 is correct in British and North American English. It is a type 1 conditional as explained here: https://www.ef.com/english-resources/english-grammar/conditional/ The structure is [if (action in the simple present tense), then (result in the simple future tense)] Choice 1 is equivalent to - If I have the lesson, then (the result will be ...). - The (result will be ...), if I have the lesson. The actual wording is 1. It will depend on whether or not I have the lesson today. which is equivalent to (the result) will depend on (if) I have the lesson today. In casual spoken and written English, people also use "it depends on ..." to express to express a type 1 conditional.

They are both correct. The first uses the phrase "will depend" , and the second phrase has it in the present tense" it depends".