No, Lindahl equilibrium is not necessarily implied by efficiency in the production of the good. Lindahl equilibrium is a concept in economics that describes a situation in which a group of individuals voluntarily agree on how to finance a public good, such as a public park or a highway. In a Lindahl equilibrium, each individual agrees to pay a price for the public good that reflects their own valuation of the good. The sum of these individual prices equals the cost of providing the public good.
Efficiency in the production of the public good refers to the idea that the good is produced at the lowest possible cost. While efficiency in production is an important consideration in the provision of public goods, it does not necessarily imply a Lindahl equilibrium. It is possible for a public good to be produced efficiently, but for individuals to disagree on how to finance it or to have different valuations of the good. In such cases, achieving a Lindahl equilibrium may require additional mechanisms, such as negotiation, voting, or regulation.