In a way, one could argue that the question answers itself when looking at the wording used. On a second glance, however, one can see that the answer is not as easy to answer as it may have seemed initially.
A state of lawlessness means that there are no laws in place. Laws form the regulatory frame within a society, which serves as guidance and support in order to help people know what they can or cannot do. In a state of lawlessness, however, this guiding framework has been removed. In this case, people are no longer subjected to any rules, laws or limitations to their actions.
With regard to the rights of people, this means that there are no longer laws in place that serve to protect these rights. For example, theoretically, if it is suddenly not a punishable offense to steal somebody else’s property, then that means people could lose their economic right of owning their goods. However, just because there is no law in place anymore to protect ownership, this does not necessarily mean that people actually lose the right of ownership or that their ownership is under threat—it is just not protected any longer by law.
If people use their own moral compass to figure out what's right and wrong, then in this example that would mean the right of ownership could still be upheld even without a law, as the individual’s moral awareness would uphold this right regardless. As long as people are not morally corrupt, but instead follow basic human values and morals, then one could argue that the absence of laws will not necessarily lead to a loss of the rights of the people. If anything, in some countries, where certain laws still protect racial segregation or unequal treatment of women, for example, a loss of laws would actually add rights for some people.