How can the trityl tetrafluoroborate function as a Lewis-acid catalyst Trityl tetrafluoroborate is a reagent sometimes used in synthesis as a very mild Lewis acid catalyst, and recently I've been (unsuccessfully) using it in some protecting group chemistry.  Several other uses are mentioned in eROS: 


  ...for various transformations, e.g. the Mukaiyama-type aldol reaction using a dithioacetal and silyl enol ether. It has also been used as the catalyst for the formation of glycosides from alcohols and sugar dimethylthiophosphinates and for the formation of disaccharides from a protected α-cyanoacetal of glucose and a 6-O-trityl hexose. Michael additions of various silyl nucleophiles to conjugated dithiolenium cations also proceed well. Finally, the [4 + 2] cycloaddition of cyclic dienes and oxygenated allyl cations has been effected with trityl fluoroborate.
  
  Ref: Encyclopaedia of Reagents for Organic Synthesis


Clearly, the trityl cation could act as a Lewis acid catalyst (or at least its reactivity suggests that it does), and indeed it has a vacant p-orbital allowing it to accept an electron pair (the IUPAC gold book definition being a molecular entity that is an electron-pair acceptor).

What makes less sense to me is the 'mechanism' this catalysis occurs by. The cation itself is pseudo-stable (relative to a standard planar carbocation intermediate such as that observed in an SN2 reaction)  since the aromatic rings are able to stabilise the positive charge, but even if it did react, surely one would expect this to be irreversible, such that a nucleophile would attack the vacant p-orbital to form a stable compound, killing off the reaction. 

To give an example of this, trityl tetrafluoroborate may be used to protect an alcohol with a DMB protecting group. What isn't observed is the alcohol attacking the cation to form an O-trityl bond (the trityl group itself is sometimes seen as a protecting group).
One point is that you're assuming that the "p" orbital in the center is the Lewis acidic site. This may not be the case, you can draw a resonance structure that breaks aromaticity but puts the cation at the para position of the phenyl ring. For example, the ortho and para positions are known hydride acceptors (link).

Another issues to consider is that the phenyls are bulky enough that they can't even remain coplanar.

So we can return to your issue of reversibility by looking at trityl via these two properties:


If the Lewis acidic site is via one of the phenyl rings, then the resultant adduct is destabilized by breaking aromaticity. It may be kinetically accessible and allow the trityl ion to serve as a Lewis acid, but the adduct is not stable.
If you do create an adduct with the central carbon, this adduct is greatly destabilized by steric repulsion. Enough so that fragmentation becomes likely.


In both cases, there is a kinetically accessible Lewis acid/Lewis base adduct, but this adduct has some kind of feature that makes it thermodynamically less stable. Therefore, the trityl ion can serve a catalytic role as a Lewis acid.

The exact mechanism of action (1) or (2) is likely dependent on the exact reaction you're looking at.