Chemistry - Why does lithium forms no ethynide on reacting with ethyne?

Solution 1:

Sodium alkynide was formed by reacting sodium and acetylene but in case of lithium alkynide, it can be formed by reacting acetylene with organolithium reagents like BuLi, Lithium amide, LiHMDS. From wikipedia:

Lithium amide, LiHMDS, or organolithium reagents, such as butyllithium, are frequently used form lithium acetylides:

$\ce{H-C#C-H + BuLi ->[THF][-78℃] Li -#-H + BuH}$

The above process is well described in this paper which @Tyberius linked in the comment section.

Solution 2:

Lithium actually can be reacted with acetylene to produce the ethynide:

In the laboratory samples may be prepared by treating acetylene with a solution of lithium in ammonia, on −40°C, with creation of addition compound of $\ce{Li2C2 • C2H2 • 2NH3}$ that decomposes in stream of hydrogen at room temperature giving white powder of $\ce{Li2C2}$.

$\ce{C2H2 + 2Li -> Li2C2 + H2}$

However,

Samples prepared in this manner generally are poorly crystalline.

Various alternatives are therefore often preferred, and (some of) these are also given in the Wikipedia article, and by Nilay Ghosh in his answer.