Talk to an LM class trainer and choose the "Barter Items" option in their menu. That will open a menu in which you can buy any LM pet, both combat and non-combat, for Mithril Coins (which in turn you can buy in the Store for TP). The Mithril Coin cost is roughly equivalent to the former TP cost or a bit less expensive if you buy your Mithril Coins in bulk. You'll receive a talisman item which will be auto-consumed if your character can learn the associated pet skill, so keep an eye on your chatbox for verification you got a new pet. If the pet is not added to your quickslots automatically, check your Skills tab to find it.
As an aside to the OP: With Helm's Deep all classes received a massive revamp. As a result, LMs now have to be level 15 before they can learn any of the Raven skills, but they get the Bear at level 1 to make up for that. The minimum levels for some other pets have also been changed and the Eagle is only available if you invest into the blue trait-tree (Keeper of Animals). Another noticeable effect for low-level LMs is that the emergency heal "Wisdom of the Council" now becomes available at level 30 instead of level 20.
German, female, migrated from CodeMasters in 2011, Premium member, slow-leveller, pure PvEer and opposed to Forced Emotes - wherever I fit into the statistic, it's not in its middle.