In the past, we've looked at how lassen expresses "to let" and "to leave," and how lassen is used in combination with other verbs. But there are also many verbs that use lassen as a root. 

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This is by no means an exhaustive list, but instead a number of examples that are very common. Let's go alphabetically, starting with (jemanden) entlassen, which can refer to releasing someone from an obligation, but also is a polite way of talking about firing someone from a job. 

Eigentlich hätt ich ihn entlassen müssen.

Actually, I should have fired him.

Caption 53, Großstadtrevier: Nicht mit mir

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The verb (etwas) hinterlassen means "to leave (something) behind."

Aber wenigstens hat dieser Vollidiot eine Spur hinterlassen.

But at least the complete idiot left behind a trace.

Caption 59, Die Pfefferkörner: Endspurt

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The verb loslassen means "to let go," either physically or emotionally. 

Trotzdem weiß sie, dass sie ihre Kinder auch irgendwann loslassen muss.

But she knows that she must someday let go of her children.

Caption 43, Tapetenwechsel: Barbara Becker mag es aufgeräumt

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The verb nachlassen refers to something abating, fading, easing, or relenting.

Deswegen hat's in den letzten Wochen bisschen nachgelassen... in den letzten Jahren.

That's why it's declined a little over the past few weeks... over the past few years.

Caption 15, Formel-1-Rennfahrer: Timo Glock

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The verb (etwas) veranlassen means "to arrange (something)."

Ja, das können wir für Sie veranlassen.

Yes, we can arrange that for you.

Caption 74, Galileo: So hart ist der Job im Callcenter

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One essential verb is verlassen, which is different from lassen in that it specifically means "to leave" in the sense of departing from a place or abandoning someone or something. It also requires a direct object.

Ich möchte Sie bitten, dann die Fähre zu verlassen.

I would like to ask you to then leave the ferry.

Caption 19, Die Pfefferkörner: Abschied tut weh

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Ich will ihn auch gar nicht verlassen.

I really don't want to leave him.

Caption 69, Die Pfefferkörner: Abschied tut weh

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And finally, we come to zulassen, which means "to permit" or "to allow." 

Aber Theresa, wir können nicht zulassen, dass die beiden gewinnen.

But Theresa, we can't let the two of them win.

Captions 23-24, Heidi Schatzdiebe

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Einundsechzig Komma fünf Millionen Kfz sind in Deutschland zugelassen.

Sixty-one point five million motor vehicles are registered in Germany.

Caption 2, Richter Alexander Hold: Richtig parken

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Further Learning
You can find examples of these verbs, as well as others that have the root lassen, on Yabla German. One additional expression you can look up is sich auf jemanden verlassen.