So after digging a bit, Images of America, Naval Air Station, Lakehurst has this excerpt:

In this 1916 view, men test-fire Eddystone shells made for the Russian government. Despite imperial Russian army inspectors stationed at Lakehurst between 1915 and 1917, there were reports that the shells shipped for use overseas were of only fair quality. However, with the United States soon to be directly involved in World War I, the Lakehurst Proving Grounds soon came under U.S. Army control.

The Eddystone Ammunition Corporation was located nearby in Eddystone, Pennsylvania.

Per the Joint Base McGuire-Dix-Lakehurst page:

Lakehurst's history begins as a munitions-testing site for the Imperial Russian Army in 1916. It was then gained by the U.S. Army as Camp Kendrick during World War 1. The Navy purchased the property in 1921 for use as an airship station and renamed it Naval Air Station Lakehurst.

And from Naval Air Systems (NAVAIR) command:

Military operations at Lakehurst began in 1916 when the Eddystone Chemical Corporation bought the first parcel of land from the Manchester Land Company with the intent of using it as an ammunition testing Ground for the Imperial Russian Army.

The U.S. Army purchased the property and named it Camp Kendrick and continued to use the facility for testing munitions shortly after entering World War I. The Navy purchased an additional 1,499 acres of the property for $14,190 for use as an airship station following the war. The base was renamed Naval Air Station (NAS) Lakehurst in 1921.

Source

So it appears that the Russians were buying ammunition for their war effort, and it was being tested at what became Lakehurst.

If you're asking whether European nations have had similar arrangements - the answer is yes! To this day in fact. Many many European nations have agreements to station troops in the US for training and testing purposes.

The German Air Force Flying Training Center is not located in Germany but instead at Holloman AFB in New Mexico. They've been training in the US since 1958.

One of the reasons listed:

There are numerous reasons the German Air Force trains here. The area offers great flying weather and has suitable air space. Other reasons are the proximity of Holloman AFB to the German Air Force Air Defense Center (GAF ADC) at Ft. Bliss, TX and the centralizing of German aircrew training for the TORNADO at a single location.

The German Air Force also has a training squadron at Naval Air Station Pensacola, in Florida.

The UK's 17(Reserve) Test and Evaluation Squadron is currently in Edwards AFB, CA is another example of foreign nations operating in the US for testing and training purposes.

Singapore has a squadron of F-16's at Luke Air Force Base in AZ, a parternship that goes back over 20 years. They also have a squadron of F-15SG's in Mountain Home AFB, ID and more:

Every two years the RSAF hosts an extremely robust exercise right here at Luke, which yields tremendous training for RSAF and many other Singapore Armed Forces units from over 9000 miles away. Additionally, our bond with our partners in the Pacific extends well beyond Luke. Singapore has a squadron of F-15SG's at Mountain Home AFB in Idaho, a squadron of Apache helicopters right down the road in Tucson, and a detachment of CH-47 Chinook helicopters in Grand Prairie Texas.