The earliest US commemorative coins were all closely associated with a World's Fair/International Exposition (things began to change with the 1918 Illinois Statehood Centennial Half Dollar). As a result, their authorization generally came not via a standalone bill, but as a provision embedded within a multi-purpose appropriation bill. The Lafayette Dollar followed such a path.
On February 6, 1899, the House Committee on Appropriations introduced the Sundry Civil Appropriations Bill for 1900. The bill covered the appropriations to be made by Congress to cover a wide range of civil expenses of the US Government not covered by other specific, independent budget appropriations for its 1900 Fiscal Year (July 1, 1899 through June 30, 1900). It was debated and amended in the House over multiple days. Ultimately, it was passed in the House on February 16th and sent to the Senate for concurrence - at this point, the bill did not include a Lafayette coin. Once received in the Senate, it was referred to its Committee on Appropriations.
The Senate Committee reported the bill out with recommended amendments. Included among the amendments was one to support the Lafayette Monument that was to be presented to France at the Paris Exposition in 1900 - it called for the minting of 50,000 silver dollar coins to be referred to as the "Lafayette Dollar." The proceeds generated from the sale of the commemorative silver dollars were to benefit the Lafayette Memorial Commission (
LMC). The various amendments were considered by the Senate, with the Lafayette Monument and coin amendment included among those passed.
Side Note: Per the March 1899 issue of the American Numismatic Association's The Numismatist magazine, the LMC originally requested 100,000 half dollars vs. 50,000 one dollar coins; it anticipated selling the commemorative 50-cent pieces for $1.00 each. Such a request, however, was never formally included in any bill or amendment considered in Congress - it appears to have been more of an informal/preliminary discussion topic vs. actual language in a bill.When the Senate-amended bill was received in the House, however, a motion was made to not concur with the Senate's changes and to request a committee of conference to resolve the differences. Though some of the disagreements were resolved via conference, disagreements remained after two different conferences were called; the Lafayette coin amendment appears not to have been threatened, however.
Eventually, the Senate receded from insisting on its remaining amendments and its disagreement over the remaining amendments put forth by the House. As a result, the appropriations bill was presented to President William McKinley and was signed into law by him on March 3, 1899. With McKinley's signature, many Government projects and expenses in FY 1900 were funded and the Lafayette Dollar was born!
1900 Lafayette Memorial Dollar

To learn more about the Lafayette Memorial Half Dollar, check out:
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1900 Lafayette Memorial Dollar-
1900 Lafayette Memorial Dollar - Revisited-
1900 Lafayette Memorial Dollar - Press Release-
1900 Lafayette Memorial Dollar - First Coin Presentation-
1900 Lafayette Memorial Dollar - Coins Depicting a Statue Thread-
1881 Yorktown Medal Design vs. 1900 Lafayette Dollar DesignFor other of my posts about commemorative coins and medals, see:
Commems Collection.