A Lie algebra is said to satisfy the Baer condition provided each of its 1-dimensional subalgebras is a subideal; if the defect is bounded then the Lie algebra is bounded Baer. We first characterise restricted enveloping algebras (of odd characteristicp) that satisfy the bounded Baer condition. Using this characterisation, we are then able to construct a Lie algebra satisfying the bounded Engel condition, in each odd characteristicp, that does not satisfy the Baer condition. Such a bounded Engel Lie algebra must contain a non-nilpotent 1-generated ideal