E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Lattice or Chequers.
A public-house sign, the arms of Fitzwarren, the head of which house, in the days of the Henrys, was invested with the power of licensing the establishments of vintners and publicans. Houses licensed notified the same by displaying the Fitzwarren arms. (The Times, April 29, 1869.)
The Fitzwarren arms were chequy or and gules, hence public-houses and their signs are still frequently called the Red Lattices.
A calls me een now, my lord, through a red lattice.Shakespeare: 2 Henry IV., ii. 2.