Lucid

adj.capable, thoughtfulprofessional

Meaning 1

Expressed so clearly that a difficult idea becomes easy to follow.

Reach for it when praising an explanation, account, or style for transparent reasoning

Her lucid summary separated the observed facts from open questions.

everyday
clear
plain broad praise for easy understanding fits
not when Clear may concern visibility and is less specific about thought or expression.
warm
plainspoken
direct familiar language creates the clarity
not when Plainspoken describes style, not the structure of an argument.
professional
coherent
parts connect in an understandable whole
not when Coherent material can still be dense or poorly explained.
formal
intelligible
the minimum claim is that meaning can be understood
not when Intelligible sets a lower bar than lucid.
literary
perspicuous
an exact rare synonym suits learned prose
not when Perspicuous is so unfamiliar that it defeats clarity for most readers.

Mentally clear and able to understand or communicate normally.

Reach for it when describing a person's state of awareness, especially in care contexts

He remained lucid and chose which relative should receive the update.

everyday
alert
wakeful responsiveness is the clinical observation
not when Alert does not guarantee coherent understanding.
professional
clearheaded
sound alert thinking matters more than expression
not when Clearheaded can imply judgment, while lucid may only mean awareness.
formal
rational
reasoned thought is established
not when Rational evaluates reasoning; it is not a casual substitute for observed mental clarity.

The definition and the example on this page are written here. The dictionaries above ground which meaning is being described, not the wording.