Choice A is the best answer. In the passage Lincoln states his belief that any laws that "continue in force, for the sake of example, they should be religiously observed"(lines 31-32,"for the sake...observed"). In this context, "observed" most nearly means followed, as Lincoln is urging citizens to heed or follow the country's laws.
Choices B, C, and D are incorrect because in the context of Lincoln advocating that laws be religiously "observed," he means those laws should be followed, not that they should be studied closely (choice B), considered at length (choice C), or merely recognized (choice D).