Thank you for your question.
In your situation what I suggest that you do is apply for reconsideration. What this means is that you write a reconsideration letter to the embassy/high commission which refused your application ie Lagos asking them to reconsider their decision.
You should write the letter in a way which refutes all the reasons mentioned in the refusal letter. You may also wish to attach documentary evidence which adds weight to your arguments and helps you prove your point.
This is a free service, but you should ensure that you use a postal service which allows you to have a record of the letter send and signed for by the embassy/highcommission upon receipt. This process usually takes around 2-3 months.
In respect of you applying again for a visitors visa, there is no limit to the amount of time that you may apply for a visa, unless you have been barred from applying. Should you wish not to submit a letter of reconsideration, you can reapply again and cover all the points on which they have refused you on and ensure that you provide evidence so they do not refuse any aspect of your appeal.
I hope this answers your question, if so kindly rate my answer positively. If however, you feel that the answer does not cover all the points raised in your question, please DO NOT rate my answer negatively, I will be happy to answer further question until you are satisfied with my answer.