lassen
to let
To allow or permit someone to do something.
Meine Eltern lassen mich am Wochenende mit Freunden ausgehen.
My parents let me go out with friends on the weekend.

to let / to have
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to let
To allow or permit someone to do something.
Meine Eltern lassen mich am Wochenende mit Freunden ausgehen.
My parents let me go out with friends on the weekend.

In many of its meanings, 'lassen' is used like a modal verb and appears with a second verb in the infinitive. This second verb always comes at the end of the sentence or clause.
Ich lasse mein Fahrrad in der Werkstatt reparieren.
I am having my bicycle repaired at the workshop.
When 'lassen' is used with a second verb in the perfect tense, a special form is created: 'haben' + infinitive + infinitive of 'lassen'. This construction is called 'Ersatzinfinitiv' (substitute infinitive) or 'doppelter Infinitiv' (double infinitive).
Sie hat mich eine Stunde warten lassen.
She made me wait for an hour.
The context determines whether 'lassen' means 'erlauben' (to allow) or 'veranlassen' (to arrange / to have something done). If it is about a person's wish, it often means 'to allow.' If it is about a paid service, it means 'to arrange / to have something done.'
Der Lehrer lässt die Schüler im Unterricht diskutieren.
The teacher lets the students discuss in class.
In the meaning 'zurücklassen' (to leave behind) or 'nicht mitnehmen' (not to take along), 'lassen' stands alone, without a second verb in the infinitive. The perfect tense is formed regularly here with 'hat gelassen'.
Oh nein, ich habe mein Handy im Auto gelassen!
Oh no, I left my phone in the car!
The construction 'sich lassen' + infinitive is a common alternative to the passive with 'können' (can). It expresses that something is possible or can be done.
Der Fleck lässt sich nicht entfernen.
The stain cannot be removed.
The meaning 'veranlassen' (to arrange / to have something done) is very often used for services that you do not perform yourself. Typical examples are 'sich die Haare schneiden lassen' (to have one's hair cut) or 'das Auto waschen lassen' (to have the car washed).
Alle zwei Jahre lasse ich meine Augen vom Arzt kontrollieren.
Every two years I have my eyes checked by the doctor.
In the imperative, 'Lass das!' (Stop that!) or 'Lass das sein!' (Stop doing that!) is used as a clear command to stop a particular action immediately.
Lass das, der Hund hat Angst vor dir!
Stop that, the dog is afraid of you!
to be able to
'können' and 'lassen' can both have to do with permission or possibility. 'können' often describes that something is possible or that someone is allowed to do something, especially in everyday speech. With people, 'lassen' more often means that someone allows another person to do something. In sentences like 'Das lässt sich öffnen' (It can be opened), 'lassen' also expresses a possibility, similar to 'Das kann geöffnet werden' (It can be opened). The words can be confused because both may sound possible in such situations. As a guide: 'können' says what is possible or allowed; 'lassen' often says who allows it or that something is made possible.

Die Eltern lassen ihr Kind länger aufbleiben, weil morgen keine Schule ist.
The parents let their child stay up longer because there is no school tomorrow.
Frau Hoffmann kann morgen mit dem Zug nach Berlin fahren.
Mrs. Hoffmann can take the train to Berlin tomorrow.