is lavish or lavishly a positive word?

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It can be either. So the context shows whether it is being admired (positive) or criticized (negative) for being lavish.

This is because "lavish" has a generous, bountiful, even "rich" type of meaning, which can make people feel envious, enjoying it, admiring it, amazed, fancy occasions, celebrations, royalty, etc. ...but sometimes that can be viewed negatively if someone is jealous, or they think that it is way too much, a waste of food or money, excessive, showing off their wealth, bragging, vain, etc.

So it can be used in a positive way, as something wonderful and impressive.

Or it can be used in a negative way, as wasteful or excessive. Or being unaware of the struggles of other people, taking things for granted, being out of touch with what is really important in life.

Sometimes it will even imply a little bit of both positive and negative meanings. Like a Prince giving lavish gifts, which are very impressive and amazing, but...money is not love, so there is nothing to win her heart. So she feels both admiration for it but is also disappointed that he is giving her gifts instead of spending more time with her. Or a lavish feast which is very impressive, but when you know people who struggle to eat enough, it can seem careless to serve more food than any person could possibly eat. So it is impressive, but also wasteful. So sometimes when "lavish" is used, the meaning can be mixed with both positive and negative reactions by different people.

So lavish things can create a complicated mixture of feelings in someone, both good and bad.