Lower puzzles banking on me? (5,7)

I believe the answer is:

stare daggers

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'lower' is the definition.
I don't know anything about this answer so I cannot tell whether it can be defined by this definition.

'puzzles banking on me?' is the wordplay.
'puzzles' becomes 'staggers' (staggering is a kind of puzzling).
'banking' is an insertion indicator.
'on me?' becomes 'reda' (I can't explain this - if you can you should give a lot more credence to this answer).
'staggers' enclosing 'reda' is 'STARE DAGGERS'.

Can you help me to learn more?

I've seen this clue in the Sydney Morning Herald.

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