Yes, the “lump in the throat” is associated with anxiety. Anxiety is associated with a cascade of events which culminate in the physical symptoms of anxiety. With a perceived threat or stressor, a part of the brain called the amygdala becomes overactive, which then activates the sympathetic nervous system, which initiates the fight-or-flight response. This cascade terminates in the adrenal glands, where adrenaline and cortisol are released, which are the stress response hormones. Within the cascade, the sympathetic nervous system increases the rate of breathing, and stimulates the increase in airflow to the lungs, to oxygenate the blood so that more oxygen can be provided to the skeletal muscles for preparation to fight or flee the perceived threat.
To make more room for the increased airflow into the lungs, the throat must expand and make way. Thereby the glottis, which is the gap in-between the vocal cords and the associated throat muscles, has to expand as wide as possible. See the illustration below for the anatomy of the larynx, which houses the glottis and vocal cords.
Now contrast the above with the act of swallowing. When food is swallowed and passes down the throat into the esophagus, the muscles at the back of the throat lift the airway, the glottis constricts, and the epiglottis closes on top of the glottis, forming a seal. This prevents food from going down the wrong pipe, into the trachea (which is only for air).
However, when you attempt to swallow during this state of anxiety, the fight-or-flight response and the activated sympathetic nervous system is telling the glottis to expand, while the act of swallowing is telling the glottis to constrict. These simultaneous, opposing signals to the glottis are what give you the feeling of the lump in the throat.