Among solid $BeC{l}_2$   and liquid $BC{l}_3$

$BC{l}_3$   is stronger Lewis acid than  $BeC{l}_2$  since B in  $BC{l}_3$  is in higher oxidation state than Be in $BeC{l}_2$  

Since $BeC{l}_2$  has polymeric structure, to act as Lewis acid some  $Be-Cl$  bonds must be broken before forming adduct which requires energy

$BeC{l}_2$   is stronger Lewis acid than  $BC{l}_3$  since  $BeC{l}_2$  has less number of electrons around Be atom than B in  $BC{l}_3$

Boron being non-metal with more electronegativity can attract lone pair strongly than Be which is metal