My leathercraft mule is currently 45, and should be reaching the Ram Mantle cap soon. However, the leap from Ram Mantles (49) to Tiger Leather (61) is one I really would rather not take. I've been trying to find a decent bridge synth that won't totally break the bank but I've had no luck.
I just did orz raptor synths until I was 51 and then did tiger leather all the way up to 60. There's really no other way to do it.
Actually there is a very nice way to get around this, but it does take extra effort and may be too late.
When I was leveling my LC mule around that level, I remember bridging the gap to Tiger Leather with High Breath Mantles. I had saved up (and stored on another mule) all my Ram Mantles and started making Fragrant Ram Skins (and slapping myself for not having skilled up on these at level 30-36) to make High Breath Mantles. Only down point to this is that you either have to now an Alchemist or have Alchemy yourself up to the level needed to make the anima required (that, and you need to invest in the 40K GP key item 'Leather Ensorcellement').
Not only did this allow me to skill up three times on the precious ingredients (once making Ram Leather, once making Ram Mantles, once making High Breath Mantles), but it also allowed me to make profit all along, since HB Mantles sold decently fast on my server and for about sixfold the price any NPC would pay for the Ram Mantle. The market has changed a lot nowadays, but still HB Mantles are selling fast on my server (about 5 a day) and for about 6-7K a piece... a lot better than the ~1K you probably got for dumping your Ram Mantles to NPC.
High Breath Mantles cap at 52 (and I took it all the way to cap).
Another option might be farming Moblin Sheep Skins in Oldton Movalpolis (if you don't mind farming). It is a bitch to get sufficient skins to drop to level LC fast, but the advantage is other stuff drops there as well (mostly desynth gear to make various metal ingots, glass fiber and such). If you go this way you have the choice between turning skins into leather (cap @52) or wool (cap @54).
As a final remark: The Black Tiger Leather recipe isn't too bad. Skins can usually be bought cheap and aplenty from AH (currently 50+ for sale on Jeuno AH at 1K a piece on my server) and with a bit of luck you can break even selling the leather again. If you decide to go farm for the skins, Battalia Downs is a good place, especially if you have Widescan and Treasure Hunter (like RNG/THF, THF/RNG or BST/THF).
With Adv. Support I'd risk a 10 level gap making Leather over bridging the gap with expensive and perhaps hard to get Raptor stuff.