I would like to know if the word "lobby" would have been used in 1890s Georgia (United States) and to what exactly this word would have referred in that time.
The entry for lobby in the Online Etymology Dictionary is:
lobby (n.) 1530s, "cloister, covered walk," from Medieval Latin laubia, lobia "covered walk in a monastery," from a Germanic source (cf. Old High German louba "hall, roof;" see lodge (n.)). Meaning "large entrance hall in a public building" is from 1590s. Political sense of "those who seek to influence legislation" is attested by 1790s in American English, in reference to the custom of influence-seekers gathering in large entrance-halls outside legislative chambers.
So, to answer your question, yes, it could be used in 1890s Georgia to refer to seeking to influence legislation. If you mean for it to be the entrance to a public building, then it is much older than that.
The oldest still-extant sense of the noun lobby is, per the OED:
A passage or corridor connected with one or more apartments in a building, or attached to a large hall, theatre, or the like; often used as a waiting-place or ante-room.
The OED’s first citation for that sense is from Shakespeare, and it continues to be used in those ways in contemporary English.
However, the extended sense of lobby seen in “the alcohol lobby” or “the anti-pollution lobby” and meaning
a sectional interest (see interest sb. (def#4)), a business, cause, or principle supported by a group of people; the group of persons supporting such an interest.
is a wholly modern one that arose only in the second half of the 20th century. The earliest provided citation for that sense in the OED dates from 1952 in The Economist. There are later citations from other periodicals like The Listener (which ceased publication in 1991) and The Telegraph.
Given that all citations are from periodicals, one might speculate that this is a “newsy” sort of sense. It would certainly be anachronistic coming from the mouth of someone portrayed as being from the 1890s in Georgia.
On the other hand, if you are looking for lobby as a verb, the thing we talk about when speaking of lobbying organizations and meaning either of:
trans. To influence (members of a house of legislature) in the exercise of their legislative functions by frequenting the lobby. Also, to procure the passing of (a measure) through Congress by means of such influence. Also transf.
intr. To frequent the lobby of a legislative assembly for the purpose of influencing members’ votes; to solicit the votes of members.
Then those sorts of uses arose during the earlier half of the 19th century in the United States, and so would not necessarily seem out of place in your chosen milieu.
The US Library of Congress has made available millions of pages of newspapers in their Chronicling America archive, and it can be searched by state and decade.
One would expect newspapers to be a good source for the political meaning, however a search of Georgia newspapers between 1890 and 1899 strangely reveals no results at all. The same happens searching for news, so clearly there mustn't be any Georgian newspapers indexed between those dates.
Widening the search to include neighbouring states gives 278 results. Here's a few examples that show it used as a group to influence policy, and as a waiting room or hallway (which just so happen to be in the senate and White House).
Mr Palmer was probably entertaining or being entertained in the lobby when the general appropriating bill was read and passed in the senate, and he ought to read it now as a matter of information.
There has been a good deal of lobbying going on in regard this matter.
Whereas, the members of the supreme council have during its session been hounded and badgered by a large McKinley lobby, composed of members and non-members of the order, that used the most disreputable blackmailing methods to discredit the advisory board and to turn the supreme council into a McKinley ratification meeting, and, having signally failed to clear McKinley of the consequences of his pro-papal political record, to-day, alter two thirds of the delegates had started for home, attempted to take revenge by abolishing the national advisory board, and accomplished the same by a vote of 30 to 29 ;
Resolved, That we, the delegates in condemnation meeting assembled, denouuce the unwarranted interference of the paid McKinley lobby with the affairs of the order and denounce the cowardly denial by McKinley of his endorsement of the principles of the order given by him to our committee ;
There was an intensely expectant crowd of newspaper correspondents, larger than often gathered at the white house at night, waiting in the lobby outside the president's office.
The dispensary lobby invaded the hall of representatives and pursued members in the aisles. We saw one lobbyist ran after a member and catch him by his coat, eagerly appealing to him to change his vote. This nuisance became so intolerable and the confusion so great that on appeal to the chair the hall was ordered cleared. But even then the lobby did not retire, and was present to applaud a motion or a vote which told in its favor.
Copied from www.parliament.uk:
When there is a division (vote) in the House of Commons, MPs leave their seats and walk into whichever division lobby corresponds to the way they want to vote. By tradition, Aye is a 'yes' vote in divisions in the House of Commons. If MPs want to vote yes, they go into the Aye Lobby. The Aye Lobby is the room on the right of the Speaker, behind the Government benches. If they want to vote no, they go into the No Lobby. The No Lobby is the room on the left of the Speaker, behind the Opposition benches. In the House of Lords there is a Content Lobby and a Not Content Lobby.
The House of Commons has been around for a long time.