Question: Which type of GTPases is required for amino acid-dependent activation of mTORC1?

Context:
Heterodimeric Rag GTPases are required for amino-acid-mediated mTORC1 activation at the lysosome
Amino acids stimulate, in a Rag-, Ragulator-, and vacuolar adenosine triphosphatase-dependent fashion, the translocation of mTORC1 to the lysosomal surface, where it interacts with its activator Rheb
mTORC1 promotes growth in response to the availability of nutrients, such as amino acids, which drive mTORC1 to the lysosomal surface, its site of activation. How amino acid levels are communicated to mTORC1 is only recently coming to light by the discovery of a lysosome-based signaling system composed of Rags (Ras-related GTPases) and Ragulator v-ATPase, GATOR (GAP activity towards Rags), and folliculin (FLCN) complexes
The mechanistic target of rapamycin complex 1 (mTORC1) kinase is a major regulator of cell growth that responds to numerous environmental cues. A key input is amino acids, which act through the heterodimeric Rag GTPases (RagA or RagB bound to RagC or RagD) in order to promote the translocation of mTORC1 to the lysosomal surface, its site of activation
The heterodimeric Rag GTPases localize mTORC1 to lysosomes by their amino-acid-dependent interaction with the lysosomal Ragulator complex.
These new findings define the lysosome as a site of action for FLCN and indicate a critical role for FLCN in the amino acid-dependent activation of mTOR via its direct interaction with the RagA/B GTPases.
We show that LRS directly binds to Rag GTPase, the mediator of amino acid signaling to mTORC1, in an amino acid-dependent manner and functions as a GTPase-activating protein (GAP) for Rag GTPase to activate mTORC1.
Activation of mammalian target of rapamycin complex 1 (mTORC1) by amino acids is mediated in part by the Rag GTPases, which bind the raptor subunit of mTORC1 in an amino acid-stimulated manner and promote mTORC1 interaction with Rheb-GTP, the immediate activator
The Rag GTPases interact with mTORC1 and signal amino acid sufficiency by promoting the translocation of mTORC1 to the lysosomal surface, its site of activation
Amino acids stimulate mTORC1 activation at the lysosome in a manner thought to be dependent on the Rag small guanosine triphosphatases (GTPases), the Ragulator complex, and the vacuolar H(+)-adenosine triphosphatase (v-ATPase)
Heterodimeric Rag GTPases are required for amino-acid-mediated mTORC1 activation at the lysosome. 
Amino acids stimulate, in a Rag-, Ragulator-, and vacuolar adenosine triphosphatase-dependent fashion, the translocation of mTORC1 to the lysosomal surface, where it interacts with its activator Rheb. 
These new findings define the lysosome as a site of action for FLCN and indicate a critical role for FLCN in the amino acid-dependent activation of mTOR via its direct interaction with the RagA/B GTPases.
Interestingly, p62 colocalizes with Rags at the lysosomal compartment and is required for the interaction of mTOR with Rag GTPases in vivo and for translocation of the mTORC1 complex to the lysosome, a crucial step for mTOR activation.
Our results indicate that FLCN is specifically required for the amino acid-stimulated recruitment of mTORC1 to lysosomes by Rag GTPases. 
Mutation of LRS amino acid residues important for leucine binding renders the mTORC1 pathway insensitive to intracellular levels of amino acids. We show that LRS directly binds to Rag GTPase, the mediator of amino acid signaling to mTORC1, in an amino acid-dependent manner and functions as a GTPase-activating protein (GAP) for Rag GTPase to activate mTORC1.

Answer: Heterodimeric Rag GTPases are required for amino-acid-mediated mTORC1 activation at the lysosome
Amino acids act through the heterodimeric Rag GTPases (RagA or RagB bound to RagC or RagD) in order to promote the translocation of mTORC1 to the lysosomal surface, its site of activation.
Exact answer: Heterodimeric Rag GTPases