lebend
alive
Being alive; not dead.
Die Rettungskräfte konnten den vermissten Wanderer lebend bergen.
The rescue workers were able to recover the missing hiker alive.

living / alive
Loading your saved state.
alive
Being alive; not dead.
Die Rettungskräfte konnten den vermissten Wanderer lebend bergen.
The rescue workers were able to recover the missing hiker alive.

'Lebend' (living/alive) is the present participle of the verb 'leben' (to live). It functions like an adjective and literally means 'being in the state of life'. Before a noun, it is declined like a normal adjective.
Der Fischer warf den zu kleinen Fisch lebend ins Wasser zurück.
The fisherman threw the too-small fish back into the water alive.
In the meaning 'am Leben' (alive), 'lebend' (alive) often stands unchanged after the noun it refers to. This is especially common with verbs like 'finden' (to find), 'fangen' (to catch), or 'bergen' (to recover/rescue).
Die Polizei konnte den Täter lebend fassen.
The police were able to catch the perpetrator alive.
In the figurative, dynamic meaning, 'lebend' (living) is often combined with abstract nouns. Common examples are 'eine lebende Sprache' (a living language), 'eine lebende Legende' (a living legend), or 'eine lebende Tradition' (a living tradition).
Latein ist keine lebende Sprache mehr.
Latin is no longer a living language.
The expression 'bei lebendigem Leibe' (while still alive) is a fixed unit used to emphasize a terrible experience. The adjective 'lebendig' (alive) is strongly declined here and stands in the dative.
Die Hexe wurde der Legende nach bei lebendigem Leibe verbrannt.
According to legend, the witch was burned while still alive.
active
'aktiv' and 'lebend' can overlap in a figurative sense when something is not just present, but is being used or developed further. 'aktiv' fits people who do something or take part, and also things that are in operation. 'lebend' first simply means 'alive' and, figuratively, is used more for languages, traditions, or cultures that are still genuinely practiced. For a person who does a lot, you normally say 'aktiv', not 'lebend'. 'lebend' fits better when the contrast with 'dead' or 'no longer in use' is important.

In dem Dorf ist die alte Tradition noch lebend.
In the village, the old tradition is still alive.
Meine Schwester ist im Sportverein sehr aktiv.
My sister is very active in the sports club.