sich lichten
to clear
To become thinner or less dense. Often refers to fog, a forest, or hair.
Der Nebel am Morgen begann sich langsam zu lichten.
The morning fog slowly began to clear.

to thin / clear
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to clear
To become thinner or less dense. Often refers to fog, a forest, or hair.
Der Nebel am Morgen begann sich langsam zu lichten.
The morning fog slowly began to clear.

The verb 'lichten' is derived directly from the adjective 'licht' (light, not dense) and the noun 'das Licht' (light). It literally means to make something 'lichter' (lighter / less dense), that is, to create more light or space.
Die Wolkendecke lichtete sich und die Sonne kam hervor.
The cloud cover cleared, and the sun came out.
Pay attention to the difference: 'sich lichten' is reflexive and describes a process that happens by itself. 'Etwas lichten' is transitive and means that someone actively thins something out.
Der Nebel lichtet sich langsam.
The fog is slowly clearing.
The reflexive form 'sich lichten' is often used for natural phenomena or changes in the body. Typical nouns are 'der Nebel' (the fog), 'die Wolken' (the clouds), 'das Haar' (the hair), or 'die Reihen' (the ranks/rows, e.g. of people).
Nach dem starken Regen lichteten sich die Wolken.
After the heavy rain, the clouds cleared.
The phrase 'den Anker lichten' (to weigh anchor) is a fixed expression from seafaring. It is used almost exclusively in this context and means to begin a journey by ship.
Das Kreuzfahrtschiff wird um 20 Uhr den Anker lichten.
The cruise ship will weigh anchor at 8 p.m.
to lift
'heben' and 'lichten' can both mean that something is moved upward, but only in one very specific case. 'heben' is the general word: you lift a bag, a hand, or a heavy box. 'lichten' fits here mainly in the fixed expression 'den Anker lichten' (to weigh anchor). This means that a ship pulls up the anchor and sets off. Learners may confuse the words because, with an anchor, something really is being lifted. In everyday language, however, people almost always say 'heben' or 'hochheben'; 'lichten' sounds natural only with 'Anker'.

Am frühen Morgen lichtet die Crew den Anker und fährt aus dem Hafen.
Early in the morning, the crew weighs anchor and leaves the harbor.
Tom hebt den schweren Koffer vorsichtig in den Zug.
Tom carefully lifts the heavy suitcase onto the train.