Domains in cell membrane
There are various mechanisms through which membrane proteins can remain localized in the membrane. See the below figure from MBOTC (book):

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(A) They can aggregate together so that their relative positions are constant. 
(B) They can be anchored to the Extracellular Matrix 
(C) They can be anchored to the cytoskeleton 
(D) They can be anchored via cell-cell interactions (adherens junctions, hemidesmosomes etc)
(E) Not mentioned in the figure; mentioned in the comments. Lipid rafts are membrane regions which are composed of rigid lipids like cholesterol and sphingolipids. Lipid rafts are thicker than regular membrane and do not diffuse into the latter. Some proteins are specifically anchored to/incorporated into the lipid rafts (T-Cell receptor, IgE receptor) and their relative position with adjacent proteins (co-receptors) remains constant.


  Why is the noncytosolic layer not able to do lateral movements between
  domains but cytosolic layer is able to do so?


Where did you read this. Both layers can do lateral movements; if proteins are specifically "anchored" to one side of the membrane then the concept of domain applies to that side only.