Hello. For tu, if the command is positive (ex: call the doctor) the verb is the same as what is used for 3rd person present indicative (llama) . If it is negative (ex: do not cal the doctor), the verb is 2nd person present subjunctive (llames)
refer to http://www.spanishdict.com/answers/100064/t-commands#.VZlB8vmqqko for more information
Because Duo is using the 'tú' imperative which is derived from the 3rd person indicative mood, present tense (usted), which is 'llama'. But, 'lleme' is the usted affirmative command (this is wild, I know). Some books say take the 3rd person Present Mood, present conjugation and change the 'a' to 'e'. Others say take the 1st person indicative and remove the 'O' and add an 'e'. Both ways it works out the same. But the main reason for the difference lies with Duo. It chose to use the 'Tú' instead of the 'usted'.
You can look at this link and toward the end you can see the whole conjugation for 'llamar'
Hola takyon43: It all depends on to whom you are speaking. Speaking to one person who you know and who is your friend: "Llama". Speaking to one person who you do not know or is someone with whom you use a formal tone: "Llame". Speaking to a group of people: "Llamen". [There is another form in Spain that I do not use and therefore will not comment on.] CHAU
It's true that the imperative mood is conjugated the same as the present tense of the Subjunctive Mood (aka Present Subjunctive) except the Tú Imperative,. affirmative, as it is conjugated the same as the present tense of the Initiative Mood, 3rd person singular. Therefore it would be llama. Edit: the person I was responding to :donna382364 disappeared from the discussion. Here check it out:http://www.spanishdict.com/conjugate/llamar
Sometimes it's 'al doctor' or 'un doctor' I think al doctor is very specific like if you were a resident in a small village and someone said call THE doctor there would only be one obvious call to make as the village will likely only have the one, whereas if you you were in a strange town and needed medical assistance you would say call A doctor, meaning any doctor will do.