A reasonable question, but it contains a fallacy. This is because what are referred to as the forward and reverse reactions being catalysed by different enzymes are generally not, in fact, the same overall reaction.
Consider the relationship between DNA and its constituents (or RNA or Protein or fatty acid). You may be thinking of this as:
DNA ⇌ DNA constituents
But in fact, because hydrolysis (actually a hydrolase reaction) is thermodynamically favoured, synthesis of DNA (a ligase reaction) needs to be coupled to the hydrolysis of ‘high group-transfer’ deoxynucleotide triphosphates in order to shift the equilibrium in its direction. So the two reactions are (somewhat simplistically):
DNA → n dNMP (catalysed by DNases)
n dNTP → DNA + n pyrophosphate (catalysed by DNA polymerases)
Although in certain circumstances you can force reactions of this sort into reverse, in the cell they tend to be unidirectional, and are classified accordingly.
(In this sort of ligase reaction in the cell there is a further factor affecting the observed direction. That is the presence of pyrophosphatases that catalyse the thermodynamically favourable hydrolysis of pyrophosphate to orthophosphate, removing the former.)
Coda: Is the reaction in the reverse direction from a ligase necessarily catalysed by a lyase?
Although not affecting the principle expressed in my answer, I think that the latter part of the statement quoted from the Wikipedia page that “(synthases)...belong to the group of ligases, with lyases catalysing the reverse reaction” is not generally true. As mentioned above, the enzymes catalysing the reactions in the reverse direction from ligases involved in ‘polymerization’ are generally hydrolases (EC 3.1...), not lyases (EC 4...). I couldn’t immediately find an example of a lyase that fitted this description. You can peruse the links on this authoritative page if you wish to follow this up.