Yes, the past perfect tense can be used to describe a single past event. This is when the time or period of occurrence of that particular event isn’t specified, as in this sentence “She had taken the bar examination.” Of course, when the precise time or period of occurrence of that event is specified, say last year, the simple past tense is used: “She took the bar examination last year.”
Is the use of the simple past tense in this sentence correct: “I lived in the US for three years”? Yes, it’s correct provided that that person had not continued to reside in the US at any time afterwards.
If that person continued to live in the US afterwards and moved out of the US to live elsewhere at some unspecified time or period afterwards, the past perfect tense is used to declare that fact: “I had lived in the US for three years.”
On the other hand, if that person continued to live in the US afterwards and lived elsewhere at some specified time or period afterwards, say in Germany for two years prior to the time of speaking, the past perfect tense is also used, but this time in tandem with the simple past tense for the latter action: “I had lived in the US for three years until I moved to Germany two years ago.”
Of course, if that person continued to live in the US uninterrupted from that time onwards until the time of speaking, say for a total of five years now, the present perfect progressive tense is used: “I have been living in the US for five years now.”
I hope this explanation clarifies the usage of the past perfect for you.
