I don't know, probably not very long. They don't need to make a prototype, they already build FPGA modules and have lots of FPGA products. Nothing would need to be custom built for LTC, they would simply program it.
I don't think you understand what a FPGA is, FPGA's are reprogrammable logic arrays. They can be programmed to perform any particular task. They are like rewriteable ASICS.
Scrypt is just an algorithm, any general purpose computational device of sufficient power can be programmed to handle it. There are no "physical" requirements or differences between a FPGA that solves Scrypt or one that solves SHA.
As for additional ram, they have PCI-E mounted boards meaning you could just use the host machines memory.
now we are getting into hyperbole. can you make an FPGA for scrypt, yes. Would you pay $300 for a unit that gets 100kHs, no. It'sn not if it can but if anyone really woudl use them and if the cost to develop woudl return a profit.
Using system RAM is like flying to Idaho because you want french fries. Or paris to buy a bottle of wine. Why would you when there are places much closer that can get it for your faster and cheaper. That is what GPUs were designed for. They are built with ASICs that directly access high bandwidth DDR. The demand for these boards is so high that they can make them in huge volume and keep costs down. You wan tot reinvent the wheel.
Now it is possible to build an FPGA for scrypt mining. But it wont use system RAM or DDR. I've seen the prototype in a demonstration with a scrypt like algorithm on an Altera board. But the cost puts it on par with a GPU. But it is an undertaking and to hire a team of developers and build them out makes the profit marginal. Now with LTC less profitable than BTC to mine and with the low market cap of the market is it really worth it?