You will want board(s) from Measurement Computing (MC). Any of their boards that use their standard Universal Library (UL) will work with LOR. LOR uses MC's UL to interface to the DIO cards. They have internal PCI/ISA and external USB cards. You will want one that is strictly Digital not one that is Analog. Also you want one that has high output current. Some DIO cards only put out like 2 or 3 mA and that is not enough for SSRs. You will need a card that puts out 24 mA or more.
The SSRs will need to be triggered by 5vdc. Many of them will say they are triggered by 3v to 24v or something like that.