
fürstlich
lavish
(Figurative) Extremely generous, luxurious, or elaborate; in a way that recalls the wealth and splendor of a prince.
Bei der Hochzeit wurden die Gäste fürstlich bewirtet.
At the wedding, the guests were lavishly entertained.
princely / lavish
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lavish
(Figurative) Extremely generous, luxurious, or elaborate; in a way that recalls the wealth and splendor of a prince.
Bei der Hochzeit wurden die Gäste fürstlich bewirtet.
At the wedding, the guests were lavishly entertained.

princely
(Literal) Concerning, originating from, or belonging to a prince or princess.
Die Familie besichtigte das alte fürstliche Schloss am See.
The family visited the old princely castle by the lake.
The adjective 'fürstlich' (princely/lavish) is derived from the noun 'der Fürst' (prince). It means either literally 'belonging to a prince' or, in a figurative sense, 'luxurious and generous like at a prince's court.'
Der König empfing seine Gäste in den fürstlichen Gemächern.
The king received his guests in the princely chambers.
You can recognize the meaning from the context. If the word refers to historical people or buildings (e.g., castle, family), it is meant literally. If it describes an action or a thing (e.g., eating, salary), it is meant figuratively in the sense of 'luxurious.'
Sie erhielt ein fürstliches Gehalt für ihre Arbeit. (figurativ)
She received a lavish salary for her work. (figurative)
In the figurative meaning, 'fürstlich' (lavish) is often combined with verbs of enjoyment or reward: 'fürstlich speisen' (to dine lavishly), 'fürstlich leben' (to live lavishly), 'fürstlich entlohnt werden' (to be paid handsomely), or 'jemanden fürstlich bewirten' (to entertain someone lavishly).
Nach dem Lottogewinn konnte er endlich fürstlich leben.
After winning the lottery, he could finally live lavishly.
liberal
Liberal can occasionally describe a generous manner, but it usually requires a clear context for this meaning. Fürstlich, by contrast, expresses exceptionally generous, luxurious, or elaborate treatment. For particularly lavish arrangements, fürstlich is therefore usually the better choice.

Der Gastgeber bewirtete seine Gäste mit einem fürstlichen Festessen.
The host treated his guests to a lavish feast.
Der Gastgeber schenkte den Wein mit liberaler Hand aus.
The host poured the wine with a generous hand.