Definitely. What really helps me is to write it down. It's not necessary to do so - it's still possible to remember goals even if you haven't written them down, but for me that truly cements it in my mind. As an example, I did this last night - I woke from a lucid dream and got an idea for something to try out while writing down notes on it. I wrote down the goal and kept it in mind while falling back to sleep. In my next dream I became lucid and instantly remembered the goal (to use a particular technique to "find" a forest in the dream.) I could also remember what I did right before bed as it weirdly tied into the storyline of the non-lucid part of the dream. I think that entering a lucid dream straight from waking does make it easier to remember things, but most of my lucid dreams are DILD and I mostly can remember things well when I have the intention to.

Try not to get discouraged, though, if you have lucid dreams in which you can't remember things from real life at first. Some lucids are clearer than others, and it can be easy to become absent-minded or distracted. If you forget in one dream, that certainly doesn't mean you'll never remember it in a different one, especially if you work on it, set the intention and develop your LD skills in general.

Also, setting an intention to dream about a particular thing before sleep doesn't mean that you have to focus solely on that one thought and exclude all other thoughts. Getting upset/stressed over it isn't going to help. It's not crucial to focus on the detail of his appearance. It sounds like you know it well, and our dreaming mind can recreate people or places we know in a lot of detail without us having to obsessively focus on it. Often just one small detail or word or phrase is enough in a dream to remind you of a particular thing. So if you can learn to become lucid and aware in a dream to the point where you notice and question everything, just the word "lynx" and the intention to remember can lead to the association to all the rest. Honestly, it might help to relax, and to focus on becoming more aware and lucid first. I'd write it down before sleeping, and then just keep the general idea and intention in mind without focusing too hard on it while falling asleep.