  Since their introduction in 1967, Lawson methods have achieved constant
interest in the time discretization of evolution equations. The methods were
originally devised for the numerical solution of stiff differential equations.
Meanwhile, they constitute a well-established class of exponential integrators.
The popularity of Lawson methods is in some contrast to the fact that they may
have a bad convergence behaviour, since they do not satisfy any of the stiff
order conditions. The aim of this paper is to explain this discrepancy. It is
shown that non-stiff order conditions together with appropriate regularity
assumptions imply high-order convergence of Lawson methods. Note, however, that
the term regularity here includes the behaviour of the solution at the
boundary. For instance, Lawson methods will behave well in the case of periodic
boundary conditions, but they will show a dramatic order reduction for, e.g.,
Dirichlet boundary conditions. The precise regularity assumptions required for
high-order convergence are worked out in this paper and related to the
corresponding assumptions for splitting schemes. In contrast to previous work,
the analysis is based on expansions of the exact and the numerical solution
along the flow of the homogeneous problem. Numerical examples for the
Schr\"odinger equation are included.
