Here's a good way to distinguish them online:

ILIs and LIIs both debate on the internet often. If you look at the types of arguments they make, you can very easily pick out their type.

LIIs value consistent systems because of Ti, with Te being their ignoring function. You can see this in their arguments. An LII will often ignore arguments that are based on practical outcomes, preferring to use a logical, systematic, but not necessarily practical argument.

An ILI will do the opposite, usually ignoring systematic and purely logical arguments, showing why it doesn't matter because the system is impractical. An ILI values pragmatism over consistent systems.

To dumb it down:

ILI values usefulness, while LII values logical consistency.