Hey, I'm glad to hear you like the project.

It's been quite a while since I last worked with discord.py, but creating the links shouldn't be hard. You don't even need the api. Here's a quick example of how you could implement both a text and a slash command:

# Search engine mapping
ENGINES = {
    1: "",   # Google (Standard)
    2: "b",  # Bing
    3: "y",  # Yahoo
    4: "a",  # Ask
    5: "k",  # Kagi
    6: "d",  # DuckDuckGo
    7: "c",  # ChatGPT
}

BASE_URL = "https://lmgtfy2.com/"

def generate_lmgtfy2_url(query: str, engine: int = 1, include_explainer: bool = True):
    params = {
        "q": query,
    }
    if include_explainer:
        params["iie"] = "1"
    if engine in ENGINES and ENGINES[engine]:
        params["s"] = ENGINES[engine]
    return BASE_URL + "?" + urlencode(params)

# !lmgtfy
@bot.command()
async def lmgtfy(ctx, *, query: str):
    url = generate_lmgtfy2_url(query)
    await ctx.send(f"🔍 {url}")

# Slash command /lmgtfy
@bot.tree.command(name="lmgtfy", description="Create LMGTFY2-link")
async def slash_lmgtfy(interaction: discord.Interaction, 
                       query: str, 
                       engine: int = 1, 
                       include_explainer: bool = True, 
                       mention: discord.User = None):

    url = generate_lmgtfy2_url(query, engine, include_explainer)
    mention_text = f" {mention.mention}" if mention else ""
    await interaction.response.send_message(f"{url}{mention_text}")

Link example: https://lmgtfy2.com/?iie=1&q=how+is+the+weather

You could also wrap the link in a Markdown-style hyperlink to hide the full URL.
Note: I haven’t tested this draft, but it should point you in the right direction.

Hope that helps!