We support lookup fields in SMS template e.g. you can fetch the owner information of Contact by selecting Owner from the second drop down (As Contact Owner field is of data type "Lookup(User)")

But SMS Template do not support fields with data type Lookup(User,Queue)

Lead owner is of data type Lookup(User,Queue) due to which we can't use Lead owner information directly as merge fields in SMS Template. 

As a workaround for this problem, we suggest you to pull the information (which you want to use in SMS Template) of Lead owner on Lead record itself by using formula fields and then you can use these formula fields created in SMS Template.