I posted a response that details how to make links of phrases because I believe this does address the OP’s question about context. I understood his question to be how to include sufficient context around a given link from the lesson to make it understandable both in terms of grammar and the meaning of the words.
I personally have long been altering how I make links and am less likely to click a single word. Instead, I click phrases so that I include enough of the context to make the definition of the word and its grammatical function clear. In Russian which has grammatical cases, this is particularly helpful since I am capturing a new verb and the appropriate case of the noun and adjective that are used with it. However, clicking phrases is also useful for special expressions and for grammatical patterns that are different from one’s native language.
Furthermore, because the word order in Russian is more fluid than in English, Spanish or French, the subject (noun) does not necessarily appear near the verb. If I already know the words in between, I often put in parentheses in the definition window the words that I already know which give meaning to the definition of the words that I don’t.
For example, in the definition window I have written: “(The production of traditional валенок) involves (a long process) of felting sheep wool.” In this sentence, I already knew the meaning of the Russian words in parentheses. However, the new words were “of felting sheep wool.” I wanted to include “involves” and “of felting sheep wool” together because the grammatical construction is different than in English. The word for “felt” as an adjective was new to me and appeared elsewhere in the article and I did make a link for it. However, I also wanted to make a link for the noun which means, “the making of felt” which is a single word in Russian. Although I knew the word for sheep, I didn’t know the word for wool and thus wanted to make a link that included “sheep wool.” Thus, I made a single link of the verb “involves” plus the phrase “of felting sheep wool” which gave me the grammatical structure of “involves” plus a noun plus the new words “of felting” and “wool.” A beginner may find it helpful to break these phrases and grammar into smaller chunks but that is not necessary for my present level of Russian.
Whether others would make a link the same way I did is irrelevant. My point is merely that one can include enough of a context in the definition box for each link to make the meaning of the words and their grammatical relationship to one another understandable and usable. For example, I can form other sentences with “involves” + a noun (e.g., this involves listening more) and I can use “sheep” as an adjective (e.g., sheep milk).
What is also important is that the original lesson in which I made these links is irrelevant. Rather, what is critical in terms of language learning is only what are meanings of the relevant words in a given context. For this I need to understand the grammatical structure of the phrase and how particular words are used in conjunction with certain subject matter or themes. For example, in English we say sheep wool and but we eat “lamb chops” – a different word.
In sum, what the OP wanted to accomplish is already possible in LingQ without any software change in the program. It is possible to include more of the context in the definition window so that the meaning of the words and their grammatical function are clear and usable. This is accomplished by making links of phrases and including as many other words as necessary in parentheses to make the unknown phrase comprehensible.