life / lifelong
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life
In a legal sense, it refers to life imprisonment, the most severe punishment in German criminal law.
Der Mörder wurde zu einer lebenslänglichen Haftstrafe verurteilt.
The murderer was sentenced to life imprisonment.
The word is made up of 'Leben' (life), in the form 'lebens-', and the adjective stem 'lang' (long), plus the ending '-lich'. So it literally means 'for a lifetime'.
Er hat eine lebenslängliche Garantie auf das Produkt.
He has a lifelong guarantee on the product.
'Lebenslänglich' (for life/lifelong) is very often used like an adverb without a declension ending, especially in legal contexts. It then answers the question 'Wie lange?' (for how long?).
Der Angeklagte wurde zu lebenslänglich verurteilt.
The defendant was sentenced to life.
In everyday usage, 'lebenslänglich' (life/for life) almost always refers to life imprisonment. The noun 'Haft' (imprisonment) or 'Strafe' (sentence/punishment) is often omitted because the context is clear.
Er hat für den Mord lebenslänglich bekommen.
He got life for the murder.
Outside criminal law, 'lebenslänglich' (lifelong) is often combined with rights or obligations. Typical examples are a 'lebenslängliches Wohnrecht' (lifelong right of residence) or a 'lebenslängliche Rente' (lifelong pension).
Ihre Großmutter hat ein lebenslängliches Nießbrauchrecht für das Haus.
Her grandmother has a lifelong usufruct right to the house.
permanent / lasting
'dauerhaft' and 'lebenslänglich' can both mean that something applies for a very long time. 'dauerhaft' is more general: it only says that something is not temporary. 'lebenslänglich' is more specific and means that something lasts for an entire lifetime. In everyday language, 'lebenslänglich' is used less often and often appears in fixed or serious contexts. For normal long-lasting states, 'dauerhaft' is usually more natural.
Greta bekommt wegen ihrer Krankheit lebenslänglich Unterstützung.
Because of her illness, Greta receives lifelong support.
Die neue Brücke soll dauerhaft sicher und stabil sein.
The new bridge is meant to be permanently safe and stable.