Here in western countries like Canada where I live, corporations and organizations can legally lobby an elected politician at any government job that has to do with legislation of the law. Lobbying is done by paying the elected official an agreed upon amount of money to push the organization or corporations ideas in government and law. It is not regarded the same as bribery according to law here and is intended for greater good of society but sometimes it can be used for evil. Considering this, can a Muslim run for only local or provincial elections in a secular country like Canada and can a Muslim collect lobbying payments and push their ideas if it is for the good of society and permitted under Shari'ah?

Yes if it is for the purpose of:

1- Advancing justice
2- Protecting the rights of Muslims
3- Making society a better place

That would be permissible