IIUC lutidine, which is statically hindered, is more often used when there is a trifluoromethanesulfonate leaving group, whereas imidazole, which I believe is more nucleophilic, is used when chloride is the leaving group. Let me make an educated guess: Imidazole is a nucleophilic catalyst for TBDMS chloride. However, one does not want imidazole to displace the trifluoromethanesulfonate group.
We had some problems with this reaction and purification again yesterday, which I may address on a companion thread (unless putting it into this thread would make it easier to follow). For now, I will just note that after the copper sulfate wash, we had a product that was not homogeneous. There appeared to be a light brown liquid, a whitish solid, and a purple solid. Not all of this crude product came into our chromatographic solvent, which was 4% diethyl ether in hexanes. Perhaps our wash left lutidinium trifluoromethanesulfonate with the organic, not the aqueous layer, and this was a part of the solid.
I am reconsidering copper sulfate versus HCl washes. IIRC someone thought that 1 M HCl was too strong for TBDMS groups. What if we backed off the acid strength, either by going to 0.5 M HCl, or by using a weaker acid, such as KHSO4 or the sodium form?