lel2cap_sendConnParamUpdateReq() can be used anytime when there is a connection (so outside connection up callback is OK too) with a peer device. This however is only a request from the slave to the master to change the connection parameters (only the master can change these). So the change to new parameters is not instantaneous.
The unit of the supervision timeout value is 10ms (see BT spec, host controller interface, section 7.8). Minimum value is 10 (100 ms) and it has to be larger than the max connection interval being requested, and has to be larger than (1 + slave latency) * connection interval too.
