First commissioning of the LHC lead ion beams to 1.38 A TeV beam energy was successfully achieved in November 2010. Ion collimation has been predicted to be less efficient than for protons at the LHC, because of the complexity of the physical processes involved: nuclear fragmentation and electromagnetic dissociation in the primary collimators creating fragments with a wide range of Z/A ratios, that are not intercepted by the secondary collimators but lost in the dispersion suppressor sections of the ring. In this article we present first comparisons of measured loss maps with theoretical predictions from simulation runs with the ICOSIM code. An extrapolation to define the ultimate intensity limit for Pb beams is attempted. The scope of possible improvements in collimation efficiency coming from the installation of new collimators in the cold dispersion suppressors and combined betatron and momentum cleaning is also explored.