How to interpret the lambda output struct from a linear optimization problem?

The MATLAB solve-function and several solvers in the Optimization Toolbox include the lambda-struct as an output argument.

In the documentation it is stated, that the structure contains the Lagrange Multipliers on inequality constraints, equality constraints and boundaries in separate fields.

As far as I know, the Lagrange Multipliers on the inequality constraints for an optimization problem in standard form are always >0 if the constraint is binding or zero otherwise.

Further, if I tried to solve an optimizsation problem as following, which is in non-standard form:

In the lambda-struct there is only one Lagrange Multiplier on each inequality constraint, even if they would have to broken up into two constraints in the standard-form. The Lagrange Multipliers on the inequality constraints are negative, if the upper constraint is binding and positive, if the lower constraint is binding. Is there any way to determine Lagrange multipliers on inequality constraints in the non-standard form? And how is the sign convention defined for the lambda struct?