In SQLite-net, Insert method returns the number of row inserted (SQLite.cs). So if you want it to return the last row ID you can update it to do like that.
Current implementation. 
public int Insert (object obj, string extra, Type objType)
{
    if (obj == null || objType == null) {
        return 0;
    }
    var map = GetMapping (objType);
    #if NETFX_CORE
    if (map.PK != null && map.PK.IsAutoGuid)
    {
        // no GetProperty so search our way up the inheritance chain till we find it
        PropertyInfo prop;
        while (objType != null)
        {
            var info = objType.GetTypeInfo();
            prop = info.GetDeclaredProperty(map.PK.PropertyName);
            if (prop != null) 
            {
                if (prop.GetValue(obj, null).Equals(Guid.Empty))
                {
                    prop.SetValue(obj, Guid.NewGuid(), null);
                }
                break; 
            }
            objType = info.BaseType;
        }
    }
    #else
    if (map.PK != null && map.PK.IsAutoGuid) {
        var prop = objType.GetProperty(map.PK.PropertyName);
        if (prop != null) {
            if (prop.GetValue(obj, null).Equals(Guid.Empty)) {
                prop.SetValue(obj, Guid.NewGuid(), null);
            }
        }
    }
    #endif
    var replacing = string.Compare (extra, "OR REPLACE", StringComparison.OrdinalIgnoreCase) == 0;
    var cols = replacing ? map.InsertOrReplaceColumns : map.InsertColumns;
    var vals = new object[cols.Length];
    for (var i = 0; i < vals.Length; i++) {
        vals [i] = cols [i].GetValue (obj);
    }
    var insertCmd = map.GetInsertCommand (this, extra);
    var count = insertCmd.ExecuteNonQuery (vals);
    if (map.HasAutoIncPK)
    {
        var id = SQLite3.LastInsertRowid (Handle);
        map.SetAutoIncPK (obj, id);
    }
    return count;
}
Updated implementation. 
public int Insert (object obj, string extra, Type objType)
{
    if (obj == null || objType == null) {
        return 0;
    }
    var map = GetMapping (objType);
    #if NETFX_CORE
    if (map.PK != null && map.PK.IsAutoGuid)
    {
        // no GetProperty so search our way up the inheritance chain till we find it
        PropertyInfo prop;
        while (objType != null)
        {
            var info = objType.GetTypeInfo();
            prop = info.GetDeclaredProperty(map.PK.PropertyName);
            if (prop != null) 
            {
                if (prop.GetValue(obj, null).Equals(Guid.Empty))
                {
                    prop.SetValue(obj, Guid.NewGuid(), null);
                }
                break; 
            }
            objType = info.BaseType;
        }
    }
    #else
    if (map.PK != null && map.PK.IsAutoGuid) {
        var prop = objType.GetProperty(map.PK.PropertyName);
        if (prop != null) {
            if (prop.GetValue(obj, null).Equals(Guid.Empty)) {
                prop.SetValue(obj, Guid.NewGuid(), null);
            }
        }
    }
    #endif
    var replacing = string.Compare (extra, "OR REPLACE", StringComparison.OrdinalIgnoreCase) == 0;
    var cols = replacing ? map.InsertOrReplaceColumns : map.InsertColumns;
    var vals = new object[cols.Length];
    for (var i = 0; i < vals.Length; i++) {
        vals [i] = cols [i].GetValue (obj);
    }
    var insertCmd = map.GetInsertCommand (this, extra);
    var count = insertCmd.ExecuteNonQuery (vals);
    long id = 0;    //New line
    if (map.HasAutoIncPK)
    {
        id = SQLite3.LastInsertRowid (Handle);  //Updated line
        map.SetAutoIncPK (obj, id);
    }
    //Updated lines
    //return count; //count is row affected, id is primary key
    return (int)id;
    //Updated lines
}