you may clogged the column by adding a non-clear lysate. by high speed centrifuge or passing the lysate through a 0.45 filter you can avoid this problem in future.
if your Ni-NTA affinity column is based on agarose beads. you can simply extract this agarose and use it in microtube based protocols or add the agarose to a new column (there are commercial columns or you can use a syringe as you mentioned). the principle is the same but it should be set up. adding lysate, washing and Elution.
But if your columns are solid you should use another approach.
you should explain more about the brand of columns and if you are using denature or native condition.
Is your column solid and do you use a machine for your purification? If this is the case you can try to run the machine in reverse flow mode. You have to start the machine with a low flowrate and than slowy increase the flowrate, but always have a look on the pressure of the system. The pressure should not exceed the recommended preasure of the column. These column do normally use two frits, one at the bottom and one at the top, if the column is clogged most of the times the frit on the top ist clogged and with the reverse flow methode you have the change to wash these contaminations.
If you use the gravity flow method with a self packed column i would follow the steps Mohammad-Hosein Khani suggested.
I can understand your problem and it is quite possible to use a syringe as column for purification. Columns, available in the market contains porous discs that hold your resin. In place of this you can use glass wool (preferable) or simply cotton to hold your gel bed and this will allow lysate to pass through it.
The plastic sheets to make the frits are available from Bel-Art Products (https://www.belart.com/fritware-porous-polyethylene-sheets.html).
In the long run, it is better to repack your column: Remove the gel from the column, wash with plenty of buffer (do NOT use a magnetic stirrer, as this would break the beads), decant from the fines and then pour the gel back into the column, using a reservoir. Make sure that the frits at the entrance and exits of the column are clean. See https://www.sigmaaldrich.com/content/dam/sigma-aldrich/docs/Sigma-Aldrich/General_Information/1/ge-gel-filtration.pdf for a detailed protocol.
Sometimes it helps to wash the column with 1 M NaOH, preferably the flow should be in the opposite direction from normal use.
All samples should be freed from particulate matter either by centrifugation or by filtration before loading them on a column.