Recover iCloud data from lost device
It sounds like the account is protected with two-factor authentication.
According to the FAQ on Apple's information about two-factor authentication

What if I don’t have access to a trusted device or didn't receive a verification code?
If you're signing in and don’t have a trusted device handy that can display verification codes, you can have a code sent to your trusted phone number via text message or an automated phone call instead. Click Didn't Get a Code on the sign in screen and choose to send a code to your trusted phone number.

You mentioned that the phone number is still the same, however, the normal SMS option is not working, so I would try the phone call method instead.
There is more information about how to get a verification code and sign in with two-factor authentication available at https://support.apple.com/en-us/HT204974.
Should these options still not work, you can request account recovery to regain access to your account.