Easiest way to think about it is the first word of lower high is “lower”.
Which means what? what is lower?
It is refering to the High which is the second word.
If you forget about the ranges of open high low and close, when a person is refering to a lower high. They are talking about, looking at the high of each candle whether that be for minute, hour, day, week, month or year. Is irrevelant.
They are looking at the highs [U]only[/U] of that stock or currency for whatever timeframe. and making the observation that the current high is lower than the previous high
Down day would be a lower high, day one high of 100, day two high of 99
Up day would be a higher high, day one high of 99, day two high of 100
All mean the same thing it is lower than the previous point it was at.
Think that is as basic as I can think to describe it.