A padded textile liner can be seen for example in the English Pot Helmet No. 1835.
A Leather suspensor is well visible among others in the Great Helm No. 3003.
An adjustable leather helmet liner (or suspension), so called parachute is also available separately (item No. 3673).
The advantage of the leather liner is its higher durability and the possibility to adjust its size, if the helmet does not fit perfectly. But compared to the textile liner, to wear it on bald head is not pleasant. You get pressure sores on your scalp and to talk about comfort of wear would be pure exaggeration. For a more comfortable wear you should at least put on a textile cap or better a quilted arming cap.
In contrast, a helmet equipped with padded textile liner can be worn directly the head, only it can´t be adjusted. You can reach for a cloth cap or quilted arming cap again when the helmet is loose. If it is too tight, you have to change for a higher size.