According to the article "Lysander Spooner:Right-Libertarian or Libertarian Socialist?", Lysander Spooner "was a left libertarian who was firmly opposed to capitalism." (http://au.spunk.org/library/intro/faq/sp001547/secG7.html) While Spooner was no free-market capitalist, nor an anarcho-capitalist, he was not as opposed to capitalism as most socialists were.
Firstly, Spooner's own writings do not completely support anarcho-socialism. In Natural Law, he states that:
These conditions are simply these: viz., first, that each man shall do, towards every other, all that justice requires him to do; as, for example, that he shall pay his debts, that he shall return borrowed or stolen property to its owner, and that he shall make reparation for any injury he may have done to the person or property of another.(Spooner 1882, Natural Law, available on-line at www.lysanderspooner.org)
Clearly, Spooner believed that human beings have the right to private property. This is a strong argument against pure socialism. Socialism, which is opposed completely to capitalism, advocates cooperation over competition. While not all socialists are against owning private property, many are, due to the fact that a property privately owned cannot be used by all.
Furthermore, Spooner believed in competition between businesses. This is evidenced by his stand against the Post Office. Spooner argued that postal service should be privatized. That is, instead of there being one central post office belonging to the government, there should be many post offices, operated by various private groups. This point of view is evidenced by Spooner's advertismenet for his own private postal service, which lasted for a few months in the spring of 1844 before police action forced Spooner to shut down his business:
The Company design, (if sustained by the public,) thoroughly to agitate the question, and test the constitutional right, of free competition in the business of carrying letters. The grounds on which they assert this right are published, and for sale (at the offices) in pamphlet form. (Spooner 1845, available at www.lysanderspooner.org)
Of course, one could argue that all anarchists believe in privatization of government owned businesses, as anarchists stand for the abolition of government. But if Spooner were a pure socialist, then he would have argued for there to be one central post office managed by the workers, rather than many private post offices competing with one another.
Despite Spooner's belief in competition and in private ownership of property, it is clear that he was a socialist in at least two ways..
Firstly, Spooner was against the idea of working for wages. That is, he did not believe people should work for others and be paid for it, but that instead workers should form voluntary associations in order to eliminate those businesses that hired wage laborers. (http://au.spunk.org/library/intro/faq/sp001547/secG7.html.) Anarcho-capitalists would disagree with this position, claiming instead that the wage laborer was trading his services to the capitalist for a certain amount of money, and that, as long as this was voluntary, there is nothing anti-freedom in it.
Secondly, Spooner argues that, while altruism should never be forced, one has a moral obligation to help others:
Man, no doubt, owes many other moral duties to his fellow men; such as to feed the hungry, clothe the naked, shelter the homeless, care for the sick, protect the defenceless, assist the weak, and enlighten the ignorant. But these are simply moral duties, of which each man must be his own judge, in each particular case, as to whether, and how, and how far, he can, or will, perform them.(Spooner 1882, Natural Law, available at www.lysanderspooner.org)
It is difficult to explain the precise way that this differs from the anarcho-capitalist position without attributing a set of philsophical beliefs to all anarcho-capitalists that some may or may not share. However, the nature of capitalism is pure competition. Therefore, the anarcho-capitalist generally would not envision a society in which people freely associated for the purpose of mutual aid, but a society where people were free to compete with one another in order to further their own lives. Therefore, while people would never be compelled by force not to aid one another, mutual aid would not be the highest value. Clearly, this indicates that, for the vast majority of anarcho-capitalists, human beings are not obligated morally to help one another, but merely to help themselves.
It is difficult to say to what degree Spooner actually opposed capitalism. The sources available on-line do not include the majority of his works; therefore, one must rely on second-hand information, such as quotations in scholarly articles.
It seems most likely that Spooner believed in some capitalistic ideas, such as the need for free competition, while maintaining that human beings had the right to disengage themselves from aspects of capitalism, such as by forming voluntary associations in order to work for themselves, rather than working for others.