Because the household registration is Lujiang, is it necessary to apply for a residence permit?

No need. Local hukou does not require a residence permit. Therefore, there is no need to apply for a residence permit because the household registration is Lujiang. Residence permit is an attempt made by some developed cities in China to learn from the "green card" system of developed countries, which has accumulated experience for China to formulate skilled migration measures and eventually form the national "green card" system of China.