Could someone please tell me if there are intellectual property laws in Nigeria and how the courts enforce such laws, if at all they do?

Does anyone know any patent attorney in Lagos, Nigeria?

Intellectual Property matters are generally within the jurisdiction of the Federal High Court. This court has various forms of enforcement with each to be determined by the nature of infringement concerned.

There are several intellectual property lawyers in Nigeria, in fact, a number practicing lawyers could even be described as intellectual property "specialists" for want of a better term. Indeed, a number of Nigerian universities -if not all- have intellectual property law in their law faculty curriculum at the undergraduate level. At a wider level, the government has created the Patents and Trademarks Office and as well as the Nigerian Copyright Commission, with each as you can decipher from their names governing the respective areas of intellectual property concerned.

Hope this is satisfactory?

Anybody have experience with patent enforcement in Nigeria? Especially between smaller companies? Is it even effective?

The starting point is the rule of law.

The Patent and Designs Act of 1990 is the governing Patent law in Nigeria and prescribes if and whose product may be granted the statutory rights.
Patent law deals with safeguarding rights over scientific/ technological inventions from outright copying to knowledgeable or unknowledgeable incorporation of already patented work and even to the incorporation of such a product that is sufficiently similar to one.

Having said all this , the proper approch to remedying infrigement is to write a letter to the party in infrigenment restating your patent rights, giving particulars of its breach and urging a desistment from such. In event of its disregard , the proper action would be a suit properly instuted in the relevant court ie fhc while suing for damages and /or lost profits.
Usually,the threat of litigation works But if it doesn't be ready for the long haul of a legal battle.

i̶̲̥̅̊n̶̲̥̅̊ addition †☺ what my learned friend said: you must own Τ̲̅ђe patent rights first before You can try †☺ enforce it