Let $X$ be a smooth variety over a field $\Bbbk$, and let $Y, Z \subset X$ be closed reduced subschemes of the same dimension, both of which are local complete intersections. Is $Y \cup Z$ necessarily a local complete intersection?



Is a union of local complete intersections, a local complete intersection?
The union of two planes in $\mathbb A^4$ which meet at a point is not Cohen--Macaulay, and so in particular not a local complete intersection. 


More generally, any smooth subvariety of a smooth variety is a local complete intersection, so any non-Cohen--Macaulay subvariety whose components are smooth gives an example of a union of local complete intersections which is not itself a local complete intersection.


[Added: Your question has the caveat "with an appropriate scheme structure"; is there any
other structure besides the reduced scheme structure on the union which you had in mind?]


