The Mark III Service and Target grips were used on all the "J" frame Mark III models, but NOT on the "V" frame Mark V models.
The same grips will interchange with the Trooper Mark III, Lawman Mark III, Metropolitan Police, and the Official Police Mark III.
The 2" Lawman used a grip unique to it and no other grip will fit it.
What you use on your Lawman 4" depends on whether you want rubber, wood, or a synthetic.
For rubber, only Pachmayr offers a grip and it's the large Presentation type.
In wood, a favorite of Colt owners is the Hogue Mono-Grip in fancy woods.
If you read the Hogue web site, these grips are available with or without finger grooves and checkering, and comes in a number of woods.
Prices are decent.
Other makers off grips for the Mark III in laminated woods.
Here's some sources: