Sorting a vector of class pointers based on two attributes?

I am trying to sort my vector of class pointers vector <Building*> company. Below is my code

sort(company.begin(), company.end(), [] (Building* lhs, Building* rhs)
{
    return (lhs->getCompanyName() > rhs->getCompanyName() && lhs->height() > rhs->height());
}); 

I am trying to sort based on two attributes in the class called getCompanyName() and height(). getCompanyName is to be alphabetically order from A to Z while height is to sorted in descending order.

The above sorting do not work.

However, if I split the two conditions up into the two below:

sort(company.begin(), company.end(), [] (Building* lhs, Building* rhs)
{
    return lhs->getCompanyName() > rhs->getCompanyName();
}); 

sort(company.begin(), company.end(), [] (Building* lhs, Building* rhs)
{
    return lhs->height() > rhs->height();
}); 

The vector will sort correctly but only based on one attribute.

Is there something wrong with my 2 attributes sorting code?

Edit:

getCompanyName() will be sorted first based on A-Z.

Only after getCompanyName() is sorted then height() will be sorted based on descending order.

An example of the sorted expected output:

Company Name: AQA
Height: 300

Company Name: AFE
Height: 200

Company Name: BAC
Height: 600

Company Name: BFE
Height: 100

Company Name: CJE
Height: 1200