Hi,
I have some lily bulbs planted in some 3 inch small pots, they have been growing but only few long leaves no stems yet.
It has been few months growing but only leaves. How long will they grow like normal lilies? When should I move them to bigger pots?

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Where did these bulbs come from - 3" pots are small for mature flowering sized bulbs - if they're offsets taken from mature bulbs, it may be several years before they're large enough to produce blooms.
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
I agree. I usually plant mine in groups pf 3 or 5 or 7 in pots at least 30" wide. That's so I can take them in to shelter over winter and protect from frosts as, in the garden I've just left, they wouldn't have survived the cold, wet winter.
"We don't stop playing because we grow old; we grow old because we stop playing." - George Bernard Shaw
The bulbs were cut from the lily plants, very tiny.
If they have to take few years to grow big, how to take care of them during the few years time?
Another query is, how long will a lily pot last usually? I mean the ones buy from the garden store? 3 years?
If they're tiny they'll be fine in 3" pots till you see roots starting to poke out of the bottom. Then you pot them into 4" pots and repeat as needed going up in pot size every time. They'll want good compost and regular watering but also good drainage to grow well and not rot.
I have kept lily bulbs for years once they are the size to go in big display pots. They get rested in a cool, dry place over winter and then top dressed and watered come spring. Works for me. When they look a bit congested I tip them out in spring and pot in fresh compost and cleaned pots, giving away spares or potting them up to grow on. 5 Firebolt bought at Chelsea 5 or 5 years ago have thus become about 40.
"We don't stop playing because we grow old; we grow old because we stop playing." - George Bernard Shaw
Thank you all.
Yes, they are bulblets. They have some leaves growing but the bulb size are still tiny, few years are long time to wait
Hope they can still survive...