Much agree with Astro regarding the medic priorities. The way I play medic is probably slightly different to others, but once you play with the same people for a while, I guess we all learn what to expect from each other's styles.
Rule 1 of medic - STAY ALIVE! (I know I break this rule sometimes - but only for a bit of fun when the situation isn't critical) ... then
Try to keep everyone topped up to base health unless someone's on fire, then over-heal priority people (active attacking/defending classes who're taking damage, other medics, etc.). I sometimes have to switch heal-targets around 2 times per second if things are 'busy'.
Be clear to you target when you're going to kritz/uber them. Problem on lazytown MP07 (and others) is all-talk, so where voice comms would be perfect in other games, it'll just let the other team prepare for the attack. You can get around this by using team-chat (maybe a key-bind that says "uber/kritz ready, prepare to go!"), or use "body language": I find that if the uber target and medic look eye-to-eye then nod, they know to be ready. Nothing worse than ubering someone who's just run out of ammo and you don't know about it.
If you're not playing medic, be aware of the medics around you that might be ready to uber you, and be ready for it.
If there's a demo/soldier/pyro deliberately hurting them self, they are doing it for a reason - to help you build your uber quicker.
Don't feel afraid/embarrassed to use defensive ubers - it might be tactically necessary to disrupt enemy ubers with your own, for example if the area you're defending doesn't have sentries built.
Because the medic spends probably 90% time building uber and healing people, I would say they need to have a much wider tactical view. Sometimes it may be necessary to abandon a near-death team-mate so you can run away/stay alive (see my "Rule 1"), or go to a different area of the map to heal another player/group if there are already other medics in your current area.
Keep an eye out for "phlog" pyros - when they get to 100% charged, taunt to activate 100% kritz for a few seconds, and
get an uber as well, the results can be somewhat messy!
Lazytown and how we play it (with all-talk on, some class limits, etc), can be quite different to other maps, so there are some tactical differences which you're bound to pick up over time.