The Cisco ASA 5585-X supports 1G SX optic modules and 10G SR SFP+ optic modules. The ASA5585-S10 requires an additional license to activate the 10GB capabilities of its two 10GB ports.
Issues may be seen when attempting to connect a X2-10GB-LX4 to a ASA5580-2X10GE-SR or SFP-10G-SR. The SR means Short Range so it may not be able to handle the output from a LX4 connector. This means you should be using a Mode Conditioning Patch (MCP) cable. A 50 micron OM3 cable may work as well.
"1. Some customers might be tempted to connect 1000BASE-LX/LH devices over short reaches of MMF jumper cables without MCP cables. There is a risk associated to this type of nonstandard deployment, especially when the jumper cable is an FDDI-grade or OM1 type. In such case the power coupled directly into a 62.5-micron fiber could be as high as a few dBm (typically 5 to 6 dBm), and if the jumper cable is short, the adjacent receiver will be saturated, causing high bit error rate, and eventually irreversibly damaged. We recommend the use of MCP, but if the customer remains reluctant to the deployment of MCP, a 5-dB attenuator for 1300nm should be used and plugged at the transmitter of the optical module on each side of the link."