This article will help you understand how a LUID is generated and how it's used to uniquely identify an instrument.
LUSID has unique identifier for every instrument, called the 'LUSID Unique Instrument Identifier' (aka 'LUID'). An instrument's LUID is generated when it is created in your instrument master inside LUSID.
All trading activity inside a portfolio is expressed in terms of these LUIDs, as are any holding statements or other generated reports. LUIDs are unique within your client.
In addition to LUIDs, instrument must also be associated with at least 1 unique market identifier (e.g. FIGI or a unique internal ID you have generated) and can be associated with as many non-unique identifiers as you like (e.g. ISIN, SEDOL, CUSIP, Ticker etc). These identifiers can also be used to reference the instrument inside LUSID.
For those instruments which can be traded at multiple locations, LUSID can assign a separate LUID for each venue. As such, the same stock will have a different LUID for every exchange it is listed.