In TP HD most methods to enter Lakebed Temple are not useful anymore due to the lack of Early Master Sword, however Pillar Clip and making it into the Loading Zone to enter the temple early is still possible.
Swim over to the left side of the entrance to the temple between the large blue pillar and the green pillar. Position yourself so that the yellow arrow on your mini-map is pointing north-west. You can use the Iron Boots to get into position and then take them off to make it a bit easier. Hold the Target button, and swim straight upwards. You should clip through the blue pillar and be able to swim into the loading zone without having to blow up the rock.
Like TPSD it is still possible to make it to the loading zone of Lakebed without Zora Armor just before you drown.
The only difference for now seems the visual cues cause of new texture work and the mashing of Iron boots to give you max speed while swimming.