In over 30 years of designing and building temporary and permanent earth retention walls, I have rarely seen treated wood used for lagging unless it is permanent, exposed lagging. Sometimes treated lagging is used when someone is worried about termites near a museum or some other "critical" building.
According to FHWA's 1976 Report No. FHWA-RD-75-130, Lateral Support Systems and Underpinning, Vol. III, Construction Methods, Page 275 & 276, Horizontal Wood Sheeting, "The material used for sheeting is commonly untreated wood. Occasionally, because of concern over future deterioration, specifications require treated wood, concrete planking, or steel sections. The issue of wood rotting is presently (1976!)controversial. Many contractors have found that even with deterioration the fabric of the wood remains intact, thus preventing earth from filling the space occupied by wood."
On Page 47, "There is a divergence of opinion among practitioners as to whether or not wood can be left in place permanently above the ground water table. Some claim that deterioration of the wood leads to lateral movement of soil and therefore ground settlement. Others point to many examples of wood remaining strong enough to provide the necessary resistance to prevent closing the space occupied by wood. Given these diverse opinions, one has no alternative other than to be conservative when adjoining structures must be protected. Therefore, the viable options are to remove lagging that would be permanently above the ground water level or to treat with chemicals to prevent future deterioration."
According to Alan Macbab's Earth Retention Systems Handbook, 2002, Page 188, "Lagging can be utilized in either temporary or permanent applications.....Permanent applications occur when lagging is the final exposed fascia for retaining walls constructed utilizing soldier piles.....When its use is permanent, it almost always is treated. Some municipalities require that temporary lagging be treated, but these are in the minority."
In Winterkorn and Fang's 1975 Foundation Engineering Handbook, Chapter 22, Underpinning, Page 630, it says, "All pit work is sheeted with 2" x 8" untreated horizontal timbers as excavation proceeds."
Schnabel Foundation Company's Specifications for a Contractor designed Tiedback Retaining Wall using Soldier beams, Lagging, Tiebacks and Concrete Facing, Section 2.20 states, "Lagging shall be untreated, non-stress graded rough cut lumber, No. 3 or better...."
I've never seen anyone not allow treated wood to remain in the ground. In over thirty years and hundreds of walls in many states, I have never removed lagging except for the upper 2 or 3 feet near finished grade. Treated or untreated, lagging is never removed and can not be removed from a soldier beam and lagging wall with a permanent concrete facing poured against the lagging.