Let \(L\) be a complete lattice. A subset of \(L\) is called algebraic if it is closed under arbitrary meets and under joins over nonempty up-directed subsets. \(\text{Sp}(L)\) denotes the set of all algebraic subsets of \(L\). An element \(x\in L\) is called way-below an element \(y\in L\) if, whenever \(y\leq\bigvee D\) for a nonempty up-directed \(D\subseteq L\), we have \(x\leq d\) for some \(d\in D\). An element \(x\in L\) is called compact if \(x\) is way-below \(x\). The complete lattice \(L\) is called Scott-continuous if every element is a join of elements way below it, and \(L\) is called algebraic if every element is a join of compact elements. Furthermore, \(L\) is called bi-algebraic if both \(L\) and its dual are algebraic. It is well known (see [G. Gierz, K. Hofmann, K. Keimel, J. Lawson, M. Mislove and D. S. Scott, Continuous lattices and domains. Encyclopedia of Mathematics and Its Applications 93. Cambridge: Cambridge University Press (2003; Zbl 1088.06001)]) that every algebraic lattice is Scott-continuous and every Scott-continuous lattice is upper continuous. The main result of the paper is the following theorem (solving a problem of [K. V. Adaricheva, V. A. Gorbunov and V. I. Tumanov, Adv. Math. 173, No. 1, 1–49 (2003; Zbl 1059.06003)]): For any Scott-continuous lattice \(L\), the lattice \(\text{Sp}(L)\) embeds into \(\text{Sp}(A)\) for some bi-algebraic distributive lattice \(A\), where the embedding preserves arbitrary meets and finite joins. In particular, \(\text{Sp}(L)\) has the so-called Jónsson-Kiefer property, i.e., any \(X\in\text{Sp}(L)\) is a join of elements which are join-prime in the principal ideal generated by \(X\).