The phrase 'not lift fingering' refers to the technique of playing a musical instrument where the fingers stay in their respective positions on the keys or frets. Although 'not lift fingering' is a widely used term, there are several synonyms that can be used to describe this technique. These include 'legato' which is an Italian term that means 'tied together'. 'Slurring' is another synonym that denotes a seamless transition between notes without any gaps or interruptions. The term 'smooth fingering' can also be used to describe the same technique, where the musician plays the notes with continuous and fluid finger movements.