Just want to say Lingard, along with Martial and Memphis, is a lot better on the left than he is on the right. He doesn't run from the right as comfortable than he does on the left. I remember the Moscow game, where he was comfortably our most threatening player, constantly running at the Moscow back four. From the academy he always used to play on the left too.
Anyway, as you said, we definitely could do with improving in that area. There's two options we could go with:
Inverted winger
A left footed player on the right. Someone who will want to cut in and either shoot or link up with the players in the middle of the park, whilst having the full back give the width. Mahrez could be an option. Not many out there that I know of that's realistic. If Leicester get CL football, which is looking very likely, then I don't even think Mahrez will be a realistic buy. Yarmelenko, maybe? Or maybe we can get Januzaj, (who I think still has a lot to offer) playing there.
Out and out winger
Sir Alex, more often than not, used to play with at least one winger who always kept the width. I think this is what we lack at the moment. Someone who is willing to hug the touchline, stretch play, and use their pace, power and trickery to get to the byline and whip crosses in. Valencia was a perfect example of this. If we can get someone like how Valencia was a few seasons ago then it'd be a great addition, in my opinion. Again, the question is, who's out there that could do this? Moura, Deulofeu, Bolasie, Mane? I guess there's more options out there, but I'm not too familiar with the other European leagues so I can't really say. I know Felipe Anderson's been mentioned a few times, but I'm not sure what he's like.
Either way, I hope that we have got our eye on a winger come the Summer, possibly two. At the moment, we have Depay, Lingard, Martial and Januzaj who are wingers - the latter two arguably better in other positions.
I mean, if you look at those four players mentioned, they're all very young, with very little experience. Three of them making their début seasons in the EPL. It's complete madness that we've ended up with that, despite all the money we've spent. That's not being disrespectful to the players, because they've done very well considering, but ideally, we need someone who's going to come in and be that special player for us. Hwoever, with us possibly failing to reach a CL spot, it could be difficult to attract that type of player.