What does it mean for an element to be mobile or immobile in plants?
Generally speaking, mobile elements are those that can be moved from older to newer tissue in the plant, while immobile ones cannot be. For example, calcium is incorporated into the cell wall, so it is immobile; it cannot be relocated later.
Plants with a deficiency of mobile elements (e.g. nitrogen) will exhibit damage to older tissues as the nutrients are moved to new growth. Conversely, plants lacking immobile elements (e.g. calcium) will exhibit stunted new growth while the older tissues stay healthy. Some elements (e.g. sulphur) fall somewhere between these two extremes.
To illustrate this concept, here is a plant with nitrogen deficiency (source). Notice how the older leaves are dying while the newer leaves are relatively normal.
Is there an official list of mobile and immobile elements?
No. You will probably have to survey the literature yourself to come up with such a list.
Why are some elements not mentioned in the sources?
Elements like Pb or Sr do not appear in either list because plants generally do not use these elements at all. Only a few elements are present in any appreciable quantity in plants. The main elements used are C, H, O, P, K, N, S, Ca, Fe, and Mg. Additionally, some other elements such as Cu, Mo, Al, and Cl are used in trace amounts as enzymatic cofactors. Si is used for structural purposes in some plants.
However, even for "useless" elements, it is possible to study how these elements are absorbed transported through a given plant. For instance, Rediske and Selders (1953) studied the absorption of strontium by bean plants using radioactive labeling, and concluded that the element was not relocated once absorbed by the plant. This would make it an immobile element.