Lynch was speaking as he joined workers on a rainy picket line at Euston station in central London on Saturday as a nationwide walkout of 20,000 members crippled services.
Workers at 14 train operators are on strike in a long-running dispute over jobs, wages and conditions.
Several health services unions, including the British Medical Association and the Royal College of Nursing (RCN), agreed to suspend industrial action after the Department of Health and Social Care (DHSC) made a new offer of payment.
Lynch said ministers in the health service talks showed little “change in attitude” and DfT ministers should follow suit to avoid strikes planned for late March.
He told the PA news agency: “We need an attitude change. We’ve already seen some of this in the health service and perhaps in teachers’ unions.
“The difference is that there are no conditions, it is new money – but our members are expected to swallow big changes in their working conditions and they are not prepared to do that to get a very modest and poor pay raise.
“For anything to move, they will have to withdraw some of the conditions they put on this proposal, and we want some new money in the payment proposal, so we’ll see what happens next week.”
He added: “They have 18 points they want us to give to the terms and conditions of our members, their employment contract, how much they are paid and how they are scheduled, how they do their work, what they receive for sick pay, what they receive for vacation pay, all kinds of things that are in a package as you would expect, they want to dilute it.
A spokesperson for the Department for Transport said: “RMT members in the Train Operating Companies are being denied a say in their own future while being forced to lose further wages through avoidable strikes.
“We ask the Executive of the RMT to put the Rail Delivery Group’s very fair offer to the democratic vote of its members, as it has done on two separate occasions for RMT members working for Network Rail.”
Passengers were advised to check before travelling, with trains starting later and ending much earlier than usual – typically between 7:30am and 6:30pm.
Nationally between 40% and 50% of rail services are expected to operate, but there will be wide variations in the network, with no service in some areas.
Services may also be disrupted on Sunday because much of the rolling stock will not be in the right depots.
Football fans and families traveling to leisure events over the weekend will be among those affected.
RMT members went on strike on Thursday and more strikes are planned for March 30 and April 1.
Breakthrough in the health union’s talks with the government came on Thursday after the DHSC put forward a one-off lump sum for 2022-23 that increases the value of NHS pay bands, as well as a permanent 5% increase in all pay points for 2023-24.