Morning,

I was wondering if anyone had some advice on disabling the email notifications in SharePoint LMS?

Thanks,
Rachel 

If LMS is a web application you can disable email notification from Central Admin.

Go to Central Administration > Application Management > Manage Web Applications

From ribbon Select the Outgoing email settings and remove the Outbounf SMTP server name and other settings.

If notification is going via a SharePoint List.
you can disable alert with the help of below powershell.

PowerShell script to Disable alerts on SharePoint list
Add-PSSnapin Microsoft.SharePoint.PowerShell ErrorAction SilentlyContinue

#Variables
$WebURL = "http://webURL"
$ListName="YourListName"

#Function to Disable All Active Alerts on a Given List
Function Disable-ListAlerts($WebURL, $ListName)
{
    #Get the Web and List objects
    $Web = Get-SPWeb $WebURL
    $List = $web.Lists.TryGetList($ListName)

    #Get All Alerts created in the list - Which are Active
    $ListAlerts = $Web.Alerts | Where-Object {($_.List.Title -eq $List.Title) -and ($_.Status -eq "ON")}

    Write-host "Total Number of Active Alerts Found in the list: $($ListAlerts.Count)" 
    
    #Iterate through each alert and turn it OFF
    foreach($Alert in $ListAlerts)
        {
            $Alert.Status="OFF"
            $Alert.Update()
            write-host "Disabled the Alert' $($Alert.Title)' Created for User '$($Alert.User.Name)'"
        }
         
    #Dispose web object
    $Web.Dispose()
}

#Call the function Appropriately to Disable or Enable Alerts 
Disable-ListAlerts $WebURL $ListName