Simple. Stop putting lettuce in your salads. I eat salad regularly and haven't had a lettuce salad in years. I don't like it in a mixed salad because it goes soggy. Occasionally I will make myself a salad which is just lettuce, a few pine nuts, and a simple salad dressing, as when you eat it alone it doesn't sog. (I went to stay with a French exchange student when I was 15, and they were so horrified at the idea of eating lettuce mixed in with other veg that they trained me for life.) The rest of the time, if I want a leafy salad I use spinach, usually baby spinach. Nice and leafy, good fresh taste, and most important of all, it doesn't go soggy. Look up some more salad recipes if you're stuck, there are loads of different types out there. Here's one of my favourites, which I think I will make for lunch now we mention it.
Small tin of chick peas
Carrot, diced
Tomato, diced
Various bits and bobs e.g. raisins, olives, sundried tomatoes (may need to watch the fat content with these)
Olive oil and lemon juice for dressing, though sometimes I will use various vinegars e.g. balsamic
Then you get the Japanese approach to salads.
Tomato
Wakame seaweed (you only need a bit, it swells up hugely when it's rehydrated)
Tofu
Sesame seeds
Dressing of sesame oil, rice vinegar and soy sauce.
My current passion, which is on hold while I'm on a lower-fat diet while they investigate me for gallstones, is a variation on Thai papaya salad. You're meant to make it with green papaya, but I couldn't get that and used ripe papaya instead. The recipe says "if you can't get green papaya, use green cabbage", so I'm being pretty inauthentic here, but who cares, the salad is out of this world. This makes quite a big salad.
1 ripe papaya, cut into chunks
8 or so snow peas or similar
1 red onion, finely chopped and blanched in boiling water for 5 min
5 button mushrooms, sliced
1/3 cup (brown) Thai rice, cooked
1 red pepper, cut into fine strips
1 tbsp crunchy peanut butter
juice of 1 lime
1 tbsp? light soy sauce
pinch cumin
dash cayenne
squeeze of garlic purée
bit of water to make up the sauce
Then there was a salad I had years ago which my mother copied from a rabbi's wife. I can't remember the exact recipe, but it involved raw broccoli, blanched red onion, mayonnaise as part of the dressing (I made it with vegan mayonnaise), and googling those ingredients will bring up lots of ideas.
My usual variation on Israeli salad goes something like this:
Diced tomato
Diced cucumber
A few black olives
Spring onion, chopped (optional)
Bit of fresh tofu, diced (a white cheese would work here too)
Za'atar
Olive oil
Salt
Lemon juice (optional)
A leafy salad, since I'm trotting out every recipe I can think of:
Baby spinach
Avocado
Tomato
A few green olives
Olive oil and lemon juice dressing
And these are fairly unimaginative salads, to be honest, there are far more veg out there which I should be using. There really is no reason to be stuck miserably prodding at a few limp tomatoes and a bit of soggy lettuce!
I did start out when I was a teenager with iceberg, which was what everybody I knew ate (this was the 70s). Then as romaine and other leafy kinds became more available, now I prefer them and think iceberg is a waste of time. I also have pet rabbits and rabbits aren't supposed to have iceberg so I don't buy it. Baby spinach I find enjoyable as well. I do get the texture thing - these days for me, though, it's more about things like onion - too crunchy AND too strong - or tomato (slimy and seeds). 
It makes them seem more like a snack, I guess, and kind of fun. Sometimes I get myself to eat lettuce more when I nom on it while I'm prepping it for the rabbits. Hee hee! I live with only one other person and we have pretty different tastes in foods so basically it's like living alone; I get to choose what I eat and not have to eat in front of other people much. That takes some of the pressure off. Although it can also result in laziness . . . right now I do need to try and eat more salad and stuff again.
