Hold on. There's more to this than you gave us in your question...
Answering 'no' to the question about previous refusals can be easily forgiven by an ECO if you had completed the other parts of the form accurately. Let's look at the form...
There's the section about Date, Country, Reason, and Reference Number wherein previous refusals are itemized. Had you filled this out they could assume that your 'No' check box was an innocuous clerical error. Somehow your question failed to mention the whole section must have been blank.
Answering 'No' and leaving the subsequent section blank cannot be reasonably attributed to a clerical error. Moreover, as an applicant with two prior applications you are in a position to be aware that you have had previous refusals. It's full on deception case closed.
Having said all of that, let's look at your question...
Firstly, what can I do to lift my 10 year ban?
Bans where Article 8 is not engaged get lifted through the process of Judicial Review. You need to instruct a solicitor from the UK Law Society to find and instruct a Barrister who is qualified to undertake advocacy work in the high court, and they will lodge a judicial review. In your case you will have an enormous amount of difficulty getting a solicitor to take your case. They need to show that they are not exploiting migrants by giving them false hopes, or they will attract an adverse comment from the Solicitors Regulatory Agency (SRA) which will be reckoned against their practicing competence. If somebody took you under client care, it's a retainer fee of about GBP 10k and about another GBP 25k in fees to prepare the case and represent it (that's a guess).
There are some landmark cases out there where bans were overturned by the high court, but their topologies and semantics are a lot different than yours. But with luck and some ponderous financial reserves and most of all persistence in finding a solicitor, maybe you can succeed.
Secondly, if I apply for a visitor visa to the USA, will the 10 years ban affect my chances of getting it?
Yes. The USA is a signatory to the Five Eyes Treaty in addition to a unique treaty with the UK. We have some stuff here in the archives about that already,
Note: if you lose in a judicial review case, the Home Office can ask the court for an order to recover their side of the costs. The risk of such an award to the respondent means you need to be really, really, REALLY sure you are going to win.
Note: see also Standard Visitor visa refusal (Deception, V3.6(b)) and procedure for reapplying
Note: further questions about judicial review should be taken to Legal. We have only limited scope for questions about it.
Note: in another answer user40416 (to whom thanks for a great answer) pointed out that Nigerian nationals have an unwieldy history of fraudulent visa applications. You would be in a position to be aware of this also and hence use extreme diligence in completing your visa application.
Note: for a general discussion about the UK Visa Sections posted to Nigeria, read this article in the TSE archives.
